LMFDB - Embedded newform 700.2.p.c.451.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(451,700)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("700.451"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.4
Character	$\chi$	$=$	700.451
Dual form			700.2.p.c.551.4

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.05472 - 0.942109i) q^{2} +(-0.450639 + 0.780530i) q^{3} +(0.224860 + 1.98732i) q^{4} +(1.21064 - 0.398687i) q^{6} +(-2.29962 + 1.30833i) q^{7} +(1.63511 - 2.30790i) q^{8} +(1.09385 + 1.89460i) q^{9} +(-3.24107 - 1.87123i) q^{11} +(-1.65249 - 0.720054i) q^{12} +2.41990i q^{13} +(3.65805 + 0.786573i) q^{14} +(-3.89888 + 0.893735i) q^{16} +(0.505515 + 0.291859i) q^{17} +(0.631220 - 3.02880i) q^{18} +(-3.07977 - 5.33433i) q^{19} +(0.0151060 - 2.38451i) q^{21} +(1.65551 + 5.02706i) q^{22} +(3.73439 - 2.15605i) q^{23} +(1.06454 + 2.31628i) q^{24} +(2.27981 - 2.55232i) q^{26} -4.67556 q^{27} +(-3.11717 - 4.27589i) q^{28} -0.435463 q^{29} +(-1.26933 + 2.19854i) q^{31} +(4.95421 + 2.73053i) q^{32} +(2.92110 - 1.68650i) q^{33} +(-0.258212 - 0.784080i) q^{34} +(-3.51922 + 2.59985i) q^{36} +(-5.65039 - 9.78676i) q^{37} +(-1.77723 + 8.52769i) q^{38} +(-1.88881 - 1.09050i) q^{39} -7.35068i q^{41} +(-2.26240 + 2.50075i) q^{42} +5.80096i q^{43} +(2.98995 - 6.86180i) q^{44} +(-5.96996 - 1.24418i) q^{46} +(-5.78826 - 10.0256i) q^{47} +(1.05940 - 3.44594i) q^{48} +(3.57652 - 6.01735i) q^{49} +(-0.455610 + 0.263046i) q^{51} +(-4.80912 + 0.544138i) q^{52} +(-1.55746 + 2.69759i) q^{53} +(4.93139 + 4.40489i) q^{54} +(-0.740624 + 7.44657i) q^{56} +5.55147 q^{57} +(0.459290 + 0.410254i) q^{58} +(-1.73534 + 3.00569i) q^{59} +(-8.99597 + 5.19383i) q^{61} +(3.41004 - 1.12299i) q^{62} +(-4.99421 - 2.92575i) q^{63} +(-2.65284 - 7.54735i) q^{64} +(-4.66981 - 0.973217i) q^{66} +(-8.52602 - 4.92250i) q^{67} +(-0.466348 + 1.07025i) q^{68} +3.88640i q^{69} +9.96771i q^{71} +(6.16112 + 0.573383i) q^{72} +(-8.48612 - 4.89946i) q^{73} +(-3.26063 + 15.6456i) q^{74} +(9.90849 - 7.31997i) q^{76} +(9.90142 + 0.0627260i) q^{77} +(0.964785 + 2.92964i) q^{78} +(-0.397549 + 0.229525i) q^{79} +(-1.17456 + 2.03439i) q^{81} +(-6.92515 + 7.75290i) q^{82} +2.59747 q^{83} +(4.74218 - 0.506159i) q^{84} +(5.46514 - 6.11837i) q^{86} +(0.196236 - 0.339892i) q^{87} +(-9.61812 + 4.42040i) q^{88} +(-8.55647 + 4.94008i) q^{89} +(-3.16604 - 5.56486i) q^{91} +(5.12447 + 6.93662i) q^{92} +(-1.14402 - 1.98149i) q^{93} +(-3.34020 + 16.0273i) q^{94} +(-4.36382 + 2.63643i) q^{96} +4.54044i q^{97} +(-9.44122 + 2.97713i) q^{98} -8.18738i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 2 q^{4} + 4 q^{8} - 16 q^{9} + 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} + 8 q^{22} + 36 q^{24} + 30 q^{26} - 2 q^{28} - 40 q^{29} - 2 q^{32} + 60 q^{36} - 8 q^{37} + 60 q^{38} + 62 q^{42}+ \cdots - 78 q^{98}+O(q^{100}) $ 32 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 - 16 * q^9 + 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 + 8 * q^22 + 36 * q^24 + 30 * q^26 - 2 * q^28 - 40 * q^29 - 2 * q^32 + 60 * q^36 - 8 * q^37 + 60 * q^38 + 62 * q^42 - 18 * q^44 + 2 * q^46 - 16 * q^49 + 36 * q^52 + 8 * q^53 + 12 * q^54 - 4 * q^56 - 48 * q^57 - 2 * q^58 + 24 * q^61 + 4 * q^64 + 24 * q^66 - 60 * q^68 - 4 * q^72 + 72 * q^73 + 38 * q^74 + 40 * q^77 - 120 * q^78 - 36 * q^81 - 42 * q^82 - 20 * q^84 + 28 * q^86 - 4 * q^88 - 60 * q^89 + 4 * q^92 + 8 * q^93 + 18 * q^94 - 60 * q^96 - 78 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.05472	−	0.942109i	−0.745798	−	0.666172i
$2$	−1.05472	−	0.942109i	−0.745798	−	0.666172i
$3$	−0.450639	+	0.780530i	−0.260177	+	0.450639i	−0.966289	−	0.257461i	$-0.917114\pi$
$3$	−0.450639	+	0.780530i	−0.260177	+	0.450639i	0.706112	+	0.708100i	$0.250447\pi$
$4$	0.224860	+	1.98732i	0.112430	+	0.993660i
$5$		0			0
$5$		0			0
$6$	1.21064	−	0.398687i	0.494242	−	0.162763i
$7$	−2.29962	+	1.30833i	−0.869175	+	0.494504i
$7$	−2.29962	+	1.30833i	−0.869175	+	0.494504i
$8$	1.63511	−	2.30790i	0.578098	−	0.815967i
$9$	1.09385	+	1.89460i	0.364616	+	0.631534i
$10$		0			0
$11$	−3.24107	−	1.87123i	−0.977218	−	0.564197i	−0.0757892	−	0.997124i	$-0.524148\pi$
$11$	−3.24107	−	1.87123i	−0.977218	−	0.564197i	−0.901429	+	0.432927i	$0.857481\pi$
$12$	−1.65249	−	0.720054i	−0.477033	−	0.207862i
$13$			2.41990i			0.671161i	0.942012	+	0.335580i	$0.108932\pi$
$13$			2.41990i			0.671161i	−0.942012	+	0.335580i	$0.891068\pi$
$14$	3.65805	+	0.786573i	0.977654	+	0.210220i
$15$		0			0
$16$	−3.89888	+	0.893735i	−0.974719	+	0.223434i
$17$	0.505515	+	0.291859i	0.122605	+	0.0707863i	0.560048	−	0.828460i	$-0.310782\pi$
$17$	0.505515	+	0.291859i	0.122605	+	0.0707863i	−0.437443	+	0.899246i	$0.644116\pi$
$18$	0.631220	−	3.02880i	0.148780	−	0.713894i
$19$	−3.07977	−	5.33433i	−0.706549	−	1.22378i	−0.966130	−	0.258057i	$-0.916918\pi$
$19$	−3.07977	−	5.33433i	−0.706549	−	1.22378i	0.259581	−	0.965721i	$-0.416416\pi$
$20$		0			0
$21$	0.0151060	−	2.38451i	0.00329639	−	0.520343i
$22$	1.65551	+	5.02706i	0.352955	+	1.07177i
$23$	3.73439	−	2.15605i	0.778674	−	0.449568i	−0.0572861	−	0.998358i	$-0.518245\pi$
$23$	3.73439	−	2.15605i	0.778674	−	0.449568i	0.835960	+	0.548790i	$0.184911\pi$
$24$	1.06454	+	2.31628i	0.217299	+	0.472809i
$25$		0			0
$26$	2.27981	−	2.55232i	0.447108	−	0.500550i
$27$	−4.67556			−0.899812
$28$	−3.11717	−	4.27589i	−0.589090	−	0.808068i
$29$	−0.435463			−0.0808634			−0.0404317	−	0.999182i	$-0.512873\pi$
$29$	−0.435463			−0.0808634			−0.0404317	+	0.999182i	$0.512873\pi$
$30$		0			0
$31$	−1.26933	+	2.19854i	−0.227978	+	0.394869i	−0.957209	−	0.289399i	$-0.906545\pi$
$31$	−1.26933	+	2.19854i	−0.227978	+	0.394869i	0.729231	+	0.684268i	$0.239878\pi$
$32$	4.95421	+	2.73053i	0.875789	+	0.482694i
$33$	2.92110	−	1.68650i	0.508499	−	0.293582i
$34$	−0.258212	−	0.784080i	−0.0442831	−	0.134469i
$35$		0			0
$36$	−3.51922	+	2.59985i	−0.586536	+	0.433308i
$37$	−5.65039	−	9.78676i	−0.928918	−	1.60893i	−0.785136	−	0.619324i	$-0.787407\pi$
$37$	−5.65039	−	9.78676i	−0.928918	−	1.60893i	−0.143782	−	0.989609i	$-0.545927\pi$
$38$	−1.77723	+	8.52769i	−0.288304	+	1.38337i
$39$	−1.88881	−	1.09050i	−0.302451	−	0.174620i
$40$		0			0
$41$		−	7.35068i		−	1.14798i	−0.818861	−	0.573992i	$-0.805394\pi$
$41$		−	7.35068i		−	1.14798i	0.818861	−	0.573992i	$-0.194606\pi$
$42$	−2.26240	+	2.50075i	−0.349096	+	0.385875i
$43$			5.80096i			0.884637i	0.896858	+	0.442319i	$0.145844\pi$
$43$			5.80096i			0.884637i	−0.896858	+	0.442319i	$0.854156\pi$
$44$	2.98995	−	6.86180i	0.450752	−	1.03446i
$45$		0			0
$46$	−5.96996	−	1.24418i	−0.880223	−	0.183444i
$47$	−5.78826	−	10.0256i	−0.844305	−	1.46238i	−0.886223	−	0.463258i	$-0.846680\pi$
$47$	−5.78826	−	10.0256i	−0.844305	−	1.46238i	0.0419181	−	0.999121i	$-0.486653\pi$
$48$	1.05940	−	3.44594i	0.152911	−	0.497379i
$49$	3.57652	−	6.01735i	0.510932	−	0.859621i
$50$		0			0
$51$	−0.455610	+	0.263046i	−0.0637981	+	0.0368339i
$52$	−4.80912	+	0.544138i	−0.666905	+	0.0754584i
$53$	−1.55746	+	2.69759i	−0.213933	+	0.370543i	−0.952942	−	0.303153i	$-0.901961\pi$
$53$	−1.55746	+	2.69759i	−0.213933	+	0.370543i	0.739009	+	0.673696i	$0.235294\pi$
$54$	4.93139	+	4.40489i	0.671078	+	0.599429i
$55$		0			0
$56$	−0.740624	+	7.44657i	−0.0989701	+	0.995090i
$57$	5.55147			0.735310
$58$	0.459290	+	0.410254i	0.0603078	+	0.0538689i
$59$	−1.73534	+	3.00569i	−0.225922	+	0.391308i	−0.956596	−	0.291419i	$-0.905873\pi$
$59$	−1.73534	+	3.00569i	−0.225922	+	0.391308i	0.730674	+	0.682727i	$0.239206\pi$
$60$		0			0
$61$	−8.99597	+	5.19383i	−1.15182	+	0.665001i	−0.949329	−	0.314284i	$-0.898236\pi$
$61$	−8.99597	+	5.19383i	−1.15182	+	0.665001i	−0.202487	+	0.979285i	$0.564902\pi$
$62$	3.41004	−	1.12299i	0.433076	−	0.142620i
$63$	−4.99421	−	2.92575i	−0.629211	−	0.368610i
$64$	−2.65284	−	7.54735i	−0.331605	−	0.943418i
$65$		0			0
$66$	−4.66981	−	0.973217i	−0.574813	−	0.119795i
$67$	−8.52602	−	4.92250i	−1.04162	−	0.601379i	−0.121327	−	0.992613i	$-0.538715\pi$
$67$	−8.52602	−	4.92250i	−1.04162	−	0.601379i	−0.920291	+	0.391234i	$0.872048\pi$
$68$	−0.466348	+	1.07025i	−0.0565530	+	0.129787i
$69$			3.88640i			0.467868i
$70$		0			0
$71$			9.96771i			1.18295i	0.806324	+	0.591475i	$0.201454\pi$
$71$			9.96771i			1.18295i	−0.806324	+	0.591475i	$0.798546\pi$
$72$	6.16112	+	0.573383i	0.726095	+	0.0675738i
$73$	−8.48612	−	4.89946i	−0.993225	−	0.573439i	−0.0869881	−	0.996209i	$-0.527724\pi$
$73$	−8.48612	−	4.89946i	−0.993225	−	0.573439i	−0.906237	+	0.422771i	$0.861058\pi$
$74$	−3.26063	+	15.6456i	−0.379041	+	1.81876i
$75$		0			0
$76$	9.90849	−	7.31997i	1.13658	−	0.839658i
$77$	9.90142	+	0.0627260i	1.12837	+	0.00714829i
$78$	0.964785	+	2.92964i	0.109240	+	0.331716i
$79$	−0.397549	+	0.229525i	−0.0447278	+	0.0258236i	−0.522197	−	0.852825i	$-0.674887\pi$
$79$	−0.397549	+	0.229525i	−0.0447278	+	0.0258236i	0.477469	+	0.878648i	$0.341554\pi$
$80$		0			0
$81$	−1.17456	+	2.03439i	−0.130506	+	0.226044i
$82$	−6.92515	+	7.75290i	−0.764755	+	0.856164i
$83$	2.59747			0.285109			0.142554	−	0.989787i	$-0.454468\pi$
$83$	2.59747			0.285109			0.142554	+	0.989787i	$0.454468\pi$
$84$	4.74218	−	0.506159i	0.517414	−	0.0552265i
$85$		0			0
$86$	5.46514	−	6.11837i	0.589321	−	0.659761i
$87$	0.196236	−	0.339892i	0.0210388	−	0.0364402i
$88$	−9.61812	+	4.42040i	−1.02529	+	0.471217i
$89$	−8.55647	+	4.94008i	−0.906984	+	0.523648i	−0.879460	−	0.475973i	$-0.842096\pi$
$89$	−8.55647	+	4.94008i	−0.906984	+	0.523648i	−0.0275247	+	0.999621i	$0.508763\pi$
$90$		0			0
$91$	−3.16604	−	5.56486i	−0.331891	−	0.583356i
$92$	5.12447	+	6.93662i	0.534263	+	0.723192i
$93$	−1.14402	−	1.98149i	−0.118629	−	0.205471i
$94$	−3.34020	+	16.0273i	−0.344515	+	1.65309i
$95$		0			0
$96$	−4.36382	+	2.63643i	−0.445381	+	0.269079i
$97$			4.54044i			0.461011i	0.973071	+	0.230506i	$0.0740380\pi$
$97$			4.54044i			0.461011i	−0.973071	+	0.230506i	$0.925962\pi$
$98$	−9.44122	+	2.97713i	−0.953708	+	0.300735i
$99$		−	8.18738i		−	0.822862i
$100$		0			0
$101$	7.91930	+	4.57221i	0.787999	+	0.454952i	0.839258	−	0.543734i	$-0.182990\pi$
$101$	7.91930	+	4.57221i	0.787999	+	0.454952i	−0.0512584	+	0.998685i	$0.516323\pi$
$102$	0.728358	+	0.151795i	0.0721182	+	0.0150299i
$103$	5.11597	+	8.86113i	0.504092	+	0.873113i	0.999989	+	0.00473128i	$0.00150602\pi$
$103$	5.11597	+	8.86113i	0.504092	+	0.873113i	−0.495897	+	0.868381i	$0.665161\pi$
$104$	5.58490	+	3.95681i	0.547645	+	0.387997i
$105$		0			0
$106$	4.18410	−	1.37790i	0.406396	−	0.133834i
$107$	5.48368	−	3.16601i	0.530128	−	0.306069i	−0.210941	−	0.977499i	$-0.567653\pi$
$107$	5.48368	−	3.16601i	0.530128	−	0.306069i	0.741068	+	0.671430i	$0.234319\pi$
$108$	−1.05134	−	9.29183i	−0.101166	−	0.894107i
$109$	9.38027	−	16.2471i	0.898467	−	1.55619i	0.0690134	−	0.997616i	$-0.478015\pi$
$109$	9.38027	−	16.2471i	0.898467	−	1.55619i	0.829454	−	0.558575i	$-0.188652\pi$
$110$		0			0
$111$	10.1851			0.966731
$112$	7.79664	−	7.15629i	0.736713	−	0.676205i
$113$	−4.17847			−0.393077			−0.196539	−	0.980496i	$-0.562970\pi$
$113$	−4.17847			−0.393077			−0.196539	+	0.980496i	$0.562970\pi$
$114$	−5.85523	−	5.23009i	−0.548393	−	0.489843i
$115$		0			0
$116$	−0.0979179	−	0.865403i	−0.00909145	−	0.0803507i
$117$	−4.58475	+	2.64701i	−0.423861	+	0.244716i
$118$	4.66198	−	1.53528i	0.429170	−	0.141334i
$119$	−1.54434	−	0.00978348i	−0.141570	−	0.000896851i
$120$		0			0
$121$	1.50301	+	2.60329i	0.136637	+	0.236663i
$122$	14.3814	+	2.99717i	1.30203	+	0.271351i
$123$	5.73743	+	3.31250i	0.517326	+	0.298678i
$124$	−4.65461	−	2.02819i	−0.417997	−	0.182137i
$125$		0			0
$126$	2.51111	+	7.79093i	0.223707	+	0.694072i
$127$			4.91036i			0.435724i	0.975980	+	0.217862i	$0.0699083\pi$
$127$			4.91036i			0.435724i	−0.975980	+	0.217862i	$0.930092\pi$
$128$	−4.31243	+	10.4596i	−0.381169	+	0.924505i
$129$	−4.52782	−	2.61414i	−0.398652	−	0.230162i
$130$		0			0
$131$	−7.93723	−	13.7477i	−0.693479	−	1.20114i	−0.970691	−	0.240332i	$-0.922744\pi$
$131$	−7.93723	−	13.7477i	−0.693479	−	1.20114i	0.277212	−	0.960809i	$-0.410590\pi$
$132$	4.00845	+	5.42594i	0.348891	+	0.472267i
$133$	14.0614	+	8.23756i	1.21928	+	0.714287i
$134$	4.35501	+	13.2243i	0.376216	+	1.14240i
$135$		0			0
$136$	1.50016	−	0.689459i	0.128637	−	0.0591206i
$137$	−3.92110	+	6.79155i	−0.335002	+	0.580241i	−0.983485	−	0.180988i	$-0.942070\pi$
$137$	−3.92110	+	6.79155i	−0.335002	+	0.580241i	0.648483	+	0.761229i	$0.275404\pi$
$138$	3.66142	−	4.09906i	0.311680	−	0.348935i
$139$	−17.4044			−1.47623			−0.738113	−	0.674677i	$-0.764283\pi$
$139$	−17.4044			−1.47623			−0.738113	+	0.674677i	$0.764283\pi$
$140$		0			0
$141$	10.4337			0.878674
$142$	9.39067	−	10.5131i	0.788048	−	0.882242i
$143$	4.52820	−	7.84307i	0.378667	−	0.655871i
$144$	−5.95805	−	6.40921i	−0.496505	−	0.534101i
$145$		0			0
$146$	4.33463	+	13.1624i	0.358736	+	1.08933i
$147$	3.08500	+	5.50324i	0.254446	+	0.453899i
$148$	18.1789	−	13.4298i	1.49429	−	1.10392i
$149$	−0.825776	−	1.43029i	−0.0676502	−	0.117174i	0.830216	−	0.557441i	$-0.188217\pi$
$149$	−0.825776	−	1.43029i	−0.0676502	−	0.117174i	−0.897867	+	0.440268i	$0.854884\pi$
$150$		0			0
$151$	6.37060	+	3.67807i	0.518432	+	0.299317i	0.736293	−	0.676663i	$-0.236575\pi$
$151$	6.37060	+	3.67807i	0.518432	+	0.299317i	−0.217861	+	0.975980i	$0.569908\pi$
$152$	−17.3469	−	1.61438i	−1.40702	−	0.130944i
$153$			1.27700i			0.103239i
$154$	−10.3841	−	9.39438i	−0.836776	−	0.757021i
$155$		0			0
$156$	1.74246	−	3.99887i	0.139509	−	0.320166i
$157$	2.66953	+	1.54125i	0.213052	+	0.123005i	0.602729	−	0.797946i	$-0.294080\pi$
$157$	2.66953	+	1.54125i	0.213052	+	0.123005i	−0.389677	+	0.920952i	$0.627413\pi$
$158$	0.635540	+	0.132451i	0.0505609	+	0.0105372i
$159$	−1.40370	−	2.43128i	−0.111321	−	0.192813i
$160$		0			0
$161$	−5.76685	+	9.84393i	−0.454491	+	0.775810i
$162$	3.15545	−	1.03915i	0.247915	−	0.0816433i
$163$	−3.91284	+	2.25908i	−0.306477	+	0.176945i	−0.645349	−	0.763888i	$-0.723288\pi$
$163$	−3.91284	+	2.25908i	−0.306477	+	0.176945i	0.338872	+	0.940833i	$0.389955\pi$
$164$	14.6082	−	1.65287i	1.14071	−	0.129068i
$165$		0			0
$166$	−2.73959	−	2.44710i	−0.212634	−	0.189932i
$167$	16.9358			1.31053			0.655266	−	0.755398i	$-0.272556\pi$
$167$	16.9358			1.31053			0.655266	+	0.755398i	$0.272556\pi$
$168$	−5.47852	−	3.93380i	−0.422677	−	0.303499i
$169$	7.14406			0.549543
$170$		0			0
$171$	6.73762	−	11.6699i	0.515238	−	0.892419i
$172$	−11.5284	+	1.30440i	−0.879029	+	0.0994596i
$173$	−0.114919	+	0.0663486i	−0.00873715	+	0.00504439i	−0.504362	−	0.863492i	$-0.668272\pi$
$173$	−0.114919	+	0.0663486i	−0.00873715	+	0.00504439i	0.495625	+	0.868537i	$0.334939\pi$
$174$	−0.527189	+	0.173613i	−0.0399661	+	0.0131616i
$175$		0			0
$176$	14.3089	+	4.39904i	1.07857	+	0.331590i
$177$	−1.56402	−	2.70897i	−0.117559	−	0.203618i
$178$	13.6788	+	2.85074i	1.02527	+	0.213672i
$179$	13.9422	+	8.04953i	1.04209	+	0.601650i	0.920424	−	0.390921i	$-0.127843\pi$
$179$	13.9422	+	8.04953i	1.04209	+	0.601650i	0.121664	+	0.992571i	$0.461177\pi$
$180$		0			0
$181$		−	3.99317i		−	0.296810i	−0.988927	−	0.148405i	$-0.952586\pi$
$181$		−	3.99317i		−	0.296810i	0.988927	−	0.148405i	$-0.0474139\pi$
$182$	−1.90343	+	8.85212i	−0.141092	+	0.656163i
$183$		−	9.36216i		−	0.692071i
$184$	1.13018	−	12.1440i	0.0833177	−	0.895267i
$185$		0			0
$186$	−0.660170	+	3.16770i	−0.0484060	+	0.232267i
$187$	−1.09227	−	1.89187i	−0.0798749	−	0.138347i
$188$	18.6225	−	13.7575i	1.35818	−	1.00337i
$189$	10.7520	−	6.11719i	0.782094	−	0.444960i
$190$		0			0
$191$	17.3638	−	10.0250i	1.25640	−	0.725385i	0.284030	−	0.958815i	$-0.408329\pi$
$191$	17.3638	−	10.0250i	1.25640	−	0.725385i	0.972373	+	0.233431i	$0.0749953\pi$
$192$	7.08640	+	1.33051i	0.511417	+	0.0960214i
$193$	9.66959	−	16.7482i	0.696032	−	1.20556i	−0.273799	−	0.961787i	$-0.588280\pi$
$193$	9.66959	−	16.7482i	0.696032	−	1.20556i	0.969832	−	0.243776i	$-0.0783862\pi$
$194$	4.27759	−	4.78888i	0.307113	−	0.343821i
$195$		0			0
$196$	12.7626	+	5.75464i	0.911615	+	0.411046i
$197$	1.63738			0.116659			0.0583293	−	0.998297i	$-0.481423\pi$
$197$	1.63738			0.116659			0.0583293	+	0.998297i	$0.481423\pi$
$198$	−7.71340	+	8.63537i	−0.548168	+	0.613689i
$199$	0.391632	−	0.678326i	0.0277621	−	0.0480853i	−0.851811	−	0.523850i	$-0.824495\pi$
$199$	0.391632	−	0.678326i	0.0277621	−	0.0480853i	0.879573	+	0.475765i	$0.157829\pi$
$200$		0			0
$201$	7.68431	−	4.43654i	0.542009	−	0.312929i
$202$	−4.04510	−	12.2832i	−0.284612	−	0.864245i
$203$	1.00140	−	0.569731i	0.0702845	−	0.0399873i
$204$	−0.625205	−	0.846294i	−0.0437731	−	0.0592524i
$205$		0			0
$206$	2.95224	−	14.1658i	0.205692	−	0.986978i
$207$	8.16972	+	4.71679i	0.567835	+	0.327839i
$208$	−2.16275	−	9.43491i	−0.149960	−	0.654193i
$209$			23.0519i			1.59453i
$210$		0			0
$211$			9.22534i			0.635099i	0.948242	+	0.317549i	$0.102860\pi$
$211$			9.22534i			0.635099i	−0.948242	+	0.317549i	$0.897140\pi$
$212$	−5.71118	−	2.48858i	−0.392246	−	0.170916i
$213$	−7.78009	−	4.49184i	−0.533083	−	0.307776i
$214$	−8.76646	−	1.82699i	−0.599263	−	0.124890i
$215$		0			0
$216$	−7.64505	+	10.7907i	−0.520180	+	0.734217i
$217$	0.0425494	−	6.71651i	0.00288844	−	0.455946i
$218$	−25.2001	+	8.29887i	−1.70677	+	0.562071i
$219$	7.64835	−	4.41578i	0.516828	−	0.298391i
$220$		0			0
$221$	−0.706272	+	1.22330i	−0.0475090	+	0.0822880i
$222$	−10.7425	−	9.59552i	−0.720986	−	0.644009i
$223$	−24.2380			−1.62310			−0.811550	−	0.584284i	$-0.801376\pi$
$223$	−24.2380			−1.62310			−0.811550	+	0.584284i	$0.801376\pi$
$224$	−14.9653	+	0.202576i	−0.999908	+	0.0135352i
$225$		0			0
$226$	4.40710	+	3.93657i	0.293156	+	0.261857i
$227$	−5.31623	+	9.20798i	−0.352851	+	0.611155i	−0.986748	−	0.162262i	$-0.948121\pi$
$227$	−5.31623	+	9.20798i	−0.352851	+	0.611155i	0.633897	+	0.773417i	$0.281454\pi$
$228$	1.24830	+	11.0325i	0.0826707	+	0.730648i
$229$	−25.5589	+	14.7564i	−1.68898	+	0.975132i	−0.733676	+	0.679499i	$0.762197\pi$
$229$	−25.5589	+	14.7564i	−1.68898	+	0.975132i	−0.955302	+	0.295633i	$0.904470\pi$
$230$		0			0
$231$	−4.51093	+	7.70009i	−0.296797	+	0.506629i
$232$	−0.712029	+	1.00501i	−0.0467470	+	0.0659819i
$233$	14.0351	+	24.3096i	0.919472	+	1.59257i	0.800218	+	0.599709i	$0.204717\pi$
$233$	14.0351	+	24.3096i	0.919472	+	1.59257i	0.119254	+	0.992864i	$0.461950\pi$
$234$	7.32940	+	1.52749i	0.479138	+	0.0998553i
$235$		0			0
$236$	−6.36348	−	2.77281i	−0.414227	−	0.180495i
$237$		−	0.413732i		−	0.0268748i
$238$	1.61963	+	1.46526i	0.104985	+	0.0949787i
$239$			13.6279i			0.881512i	0.897627	+	0.440756i	$0.145290\pi$
$239$			13.6279i			0.881512i	−0.897627	+	0.440756i	$0.854710\pi$
$240$		0			0
$241$	−3.64372	−	2.10370i	−0.234713	−	0.135512i	0.378031	−	0.925793i	$-0.376601\pi$
$241$	−3.64372	−	2.10370i	−0.234713	−	0.135512i	−0.612744	+	0.790281i	$0.709934\pi$
$242$	0.867332	−	4.16174i	0.0557542	−	0.267527i
$243$	−8.07194	−	13.9810i	−0.517815	−	0.896882i
$244$	−12.3446	−	16.7100i	−0.790283	−	1.06975i
$245$		0			0
$246$	−2.93062	−	8.89904i	−0.186850	−	0.567382i
$247$	12.9086	−	7.45276i	0.821352	−	0.474208i
$248$	2.99852	+	6.52433i	0.190406	+	0.414295i
$249$	−1.17052	+	2.02740i	−0.0741787	+	0.128481i
$250$		0			0
$251$	−18.8826			−1.19186			−0.595928	−	0.803038i	$-0.703216\pi$
$251$	−18.8826			−1.19186			−0.595928	+	0.803038i	$0.703216\pi$
$252$	4.69140	−	10.5830i	0.295531	−	0.666665i
$253$	−16.1379			−1.01458
$254$	4.62610	−	5.17905i	0.290267	−	0.324962i
$255$		0			0
$256$	14.4025	−	6.96913i	0.900155	−	0.435570i
$257$	−22.3734	+	12.9173i	−1.39561	+	0.805757i	−0.993929	−	0.110022i	$-0.964908\pi$
$257$	−22.3734	+	12.9173i	−1.39561	+	0.805757i	−0.401682	+	0.915779i	$0.631574\pi$
$258$	2.31277	+	7.02288i	0.143987	+	0.437225i
$259$	25.7981	+	15.1133i	1.60302	+	0.939092i
$260$		0			0
$261$	−0.476330	−	0.825028i	−0.0294841	−	0.0510680i
$262$	−4.58029	+	21.9777i	−0.282971	+	1.35779i
$263$	9.26400	+	5.34857i	0.571243	+	0.329807i	0.757645	−	0.652666i	$-0.226350\pi$
$263$	9.26400	+	5.34857i	0.571243	+	0.329807i	−0.186403	+	0.982473i	$0.559683\pi$
$264$	0.884043	−	9.49923i	0.0544091	−	0.584637i
$265$		0			0
$266$	−7.07012	−	21.9357i	−0.433497	−	1.34496i
$267$		−	8.90478i		−	0.544963i
$268$	7.86542	−	18.0508i	0.480457	−	1.10263i
$269$	−7.24441	−	4.18256i	−0.441699	−	0.255015i	0.262619	−	0.964900i	$-0.415414\pi$
$269$	−7.24441	−	4.18256i	−0.441699	−	0.255015i	−0.704318	+	0.709884i	$0.748747\pi$
$270$		0			0
$271$	13.5557	+	23.4791i	0.823448	+	1.42625i	0.903100	+	0.429430i	$0.141286\pi$
$271$	13.5557	+	23.4791i	0.823448	+	1.42625i	−0.0796525	+	0.996823i	$0.525381\pi$
$272$	−2.23179	−	0.686127i	−0.135322	−	0.0416025i
$273$	5.77028	+	0.0365550i	0.349234	+	0.00221241i
$274$	10.5340	−	3.46906i	0.636385	−	0.209574i
$275$		0			0
$276$	−7.72352	+	0.873895i	−0.464901	+	0.0526023i
$277$	1.67991	−	2.90970i	0.100936	−	0.174827i	−0.811134	−	0.584860i	$-0.801150\pi$
$277$	1.67991	−	2.90970i	0.100936	−	0.174827i	0.912071	+	0.410033i	$0.134483\pi$
$278$	18.3568	+	16.3969i	1.10097	+	0.983420i
$279$	−5.55380			−0.332497
$280$		0			0
$281$	−7.33947			−0.437836			−0.218918	−	0.975743i	$-0.570253\pi$
$281$	−7.33947			−0.437836			−0.218918	+	0.975743i	$0.570253\pi$
$282$	−11.0046	−	9.82966i	−0.655313	−	0.585348i
$283$	3.60282	−	6.24027i	0.214165	−	0.370945i	−0.738849	−	0.673871i	$-0.764630\pi$
$283$	3.60282	−	6.24027i	0.214165	−	0.370945i	0.953014	+	0.302926i	$0.0979635\pi$
$284$	−19.8090	+	2.24133i	−1.17545	+	0.132999i
$285$		0			0
$286$	−12.1650	+	4.00617i	−0.719332	+	0.236890i
$287$	9.61715	+	16.9038i	0.567682	+	0.997799i
$288$	0.245892	+	12.3730i	0.0144893	+	0.729089i
$289$	−8.32964	−	14.4274i	−0.489979	−	0.848668i
$290$		0			0
$291$	−3.54395	−	2.04610i	−0.207750	−	0.119944i
$292$	7.82861	−	17.9663i	0.458135	−	1.05140i
$293$			8.47879i			0.495336i	0.968845	+	0.247668i	$0.0796642\pi$
$293$			8.47879i			0.495336i	−0.968845	+	0.247668i	$0.920336\pi$
$294$	1.93085	−	8.71077i	0.112609	−	0.508022i
$295$		0			0
$296$	−31.8259	−	2.96187i	−1.84984	−	0.172155i
$297$	15.1538	+	8.74905i	0.879312	+	0.507671i
$298$	−0.476525	+	2.28652i	−0.0276044	+	0.132455i
$299$	5.21744	+	9.03686i	0.301732	+	0.522615i
$300$		0			0
$301$	−7.58959	−	13.3400i	−0.437457	−	0.768905i
$302$	−3.25404	−	9.88112i	−0.187249	−	0.568595i
$303$	−7.13749	+	4.12083i	−0.410038	+	0.236736i
$304$	16.7751	+	18.0454i	0.962120	+	1.03497i
$305$		0			0
$306$	1.20307	−	1.34687i	0.0687752	−	0.0769957i
$307$	−10.4271			−0.595104			−0.297552	−	0.954706i	$-0.596170\pi$
$307$	−10.4271			−0.595104			−0.297552	+	0.954706i	$0.596170\pi$
$308$	2.10177	+	19.6914i	0.119760	+	1.12202i
$309$	−9.22183			−0.524612
$310$		0			0
$311$	−3.96296	+	6.86404i	−0.224719	+	0.389224i	−0.956235	−	0.292600i	$-0.905480\pi$
$311$	−3.96296	+	6.86404i	−0.224719	+	0.389224i	0.731516	+	0.681824i	$0.238813\pi$
$312$	−5.60518	+	2.57609i	−0.317331	+	0.145843i
$313$	−12.5285	+	7.23333i	−0.708152	+	0.408852i	−0.810376	−	0.585910i	$-0.800737\pi$
$313$	−12.5285	+	7.23333i	−0.708152	+	0.408852i	0.102224	+	0.994761i	$0.467404\pi$
$314$	−1.36357	−	4.14058i	−0.0769507	−	0.233666i
$315$		0			0
$316$	−0.545533	−	0.738447i	−0.0306886	−	0.0415409i
$317$	1.76853	+	3.06318i	0.0993305	+	0.172046i	0.911408	−	0.411504i	$-0.134997\pi$
$317$	1.76853	+	3.06318i	0.0993305	+	0.172046i	−0.812077	+	0.583550i	$0.801663\pi$
$318$	−0.810024	+	3.88675i	−0.0454239	+	0.217958i
$319$	1.41136	+	0.814851i	0.0790212	+	0.0456229i
$320$		0			0
$321$			5.70690i			0.318528i
$322$	15.3565	−	4.94957i	0.855782	−	0.275829i
$323$		−	3.59544i		−	0.200056i
$324$	−4.30710	−	1.87677i	−0.239283	−	0.104265i
$325$		0			0
$326$	6.25524	+	1.30363i	0.346446	+	0.0722015i
$327$	8.45423	+	14.6432i	0.467520	+	0.809769i
$328$	−16.9647	−	12.0192i	−0.936717	−	0.663648i
$329$	26.4276	+	15.4820i	1.45700	+	0.853552i
$330$		0			0
$331$	−20.3773	+	11.7649i	−1.12004	+	0.646655i	−0.941411	−	0.337261i	$-0.890499\pi$
$331$	−20.3773	+	11.7649i	−1.12004	+	0.646655i	−0.178629	+	0.983917i	$0.557166\pi$
$332$	0.584065	+	5.16199i	0.0320547	+	0.283301i
$333$	12.3613	−	21.4105i	0.677397	−	1.17329i
$334$	−17.8625	−	15.9554i	−0.977393	−	0.873040i
$335$		0			0
$336$	2.07222	+	9.31041i	0.113049	+	0.507924i
$337$	−5.10057			−0.277846			−0.138923	−	0.990303i	$-0.544364\pi$
$337$	−5.10057			−0.277846			−0.138923	+	0.990303i	$0.544364\pi$
$338$	−7.53497	−	6.73049i	−0.409848	−	0.366090i
$339$	1.88298	−	3.26142i	0.102269	−	0.177136i
$340$		0			0
$341$	8.22794	−	4.75040i	0.445568	−	0.257249i
$342$	−18.1006	+	5.96087i	−0.978768	+	0.322327i
$343$	−0.351954	+	18.5169i	−0.0190037	+	0.999819i
$344$	13.3880	+	9.48520i	0.721835	+	0.511407i
$345$		0			0
$346$	0.183715	+	0.0382874i	0.00987658	+	0.00205834i
$347$	1.44316	+	0.833209i	0.0774729	+	0.0447290i	0.538236	−	0.842794i	$-0.319091\pi$
$347$	1.44316	+	0.833209i	0.0774729	+	0.0447290i	−0.460763	+	0.887523i	$0.652424\pi$
$348$	0.719599	+	0.313557i	0.0385745	+	0.0168084i
$349$			27.6081i			1.47783i	0.673801	+	0.738913i	$0.264661\pi$
$349$			27.6081i			1.47783i	−0.673801	+	0.738913i	$0.735339\pi$
$350$		0			0
$351$		−	11.3144i		−	0.603918i
$352$	−10.9475	−	18.1203i	−0.583503	−	0.965815i
$353$	−23.5193	−	13.5789i	−1.25180	−	0.722730i	−0.280337	−	0.959902i	$-0.590446\pi$
$353$	−23.5193	−	13.5789i	−1.25180	−	0.722730i	−0.971468	+	0.237172i	$0.923779\pi$
$354$	−0.902540	+	4.33067i	−0.0479695	+	0.230173i
$355$		0			0
$356$	−11.7415	−	15.8936i	−0.622300	−	0.842360i
$357$	0.703578	−	1.20100i	0.0372373	−	0.0635635i
$358$	−7.12154	−	21.6251i	−0.376385	−	1.14292i
$359$	14.5102	−	8.37747i	0.765819	−	0.442146i	−0.0655619	−	0.997849i	$-0.520884\pi$
$359$	14.5102	−	8.37747i	0.765819	−	0.442146i	0.831381	+	0.555703i	$0.187551\pi$
$360$		0			0
$361$	−9.47002	+	16.4026i	−0.498422	+	0.863293i
$362$	−3.76200	+	4.21166i	−0.197726	+	0.221360i
$363$	−2.70926			−0.142199
$364$	10.3472	−	7.54325i	0.542343	−	0.395374i
$365$		0			0
$366$	−8.82018	+	9.87444i	−0.461038	+	0.516145i
$367$	−4.22213	+	7.31294i	−0.220393	+	0.381732i	−0.954927	−	0.296839i	$-0.904067\pi$
$367$	−4.22213	+	7.31294i	−0.220393	+	0.381732i	0.734534	+	0.678572i	$0.237401\pi$
$368$	−12.6330	+	11.7437i	−0.658540	+	0.612184i
$369$	13.9266	−	8.04054i	0.724991	−	0.418574i
$370$		0			0
$371$	0.0522078	−	8.24111i	0.00271049	−	0.427857i
$372$	3.68062	−	2.71908i	0.190831	−	0.140978i
$373$	−5.18861	−	8.98694i	−0.268656	−	0.465326i	0.699859	−	0.714281i	$-0.253246\pi$
$373$	−5.18861	−	8.98694i	−0.268656	−	0.465326i	−0.968515	+	0.248955i	$0.919913\pi$
$374$	−0.630311	+	3.02443i	−0.0325926	+	0.156390i
$375$		0			0
$376$	−32.6025	−	3.03414i	−1.68134	−	0.156474i
$377$		−	1.05378i		−	0.0542723i
$378$	−17.1034	−	3.67767i	−0.879704	−	0.189159i
$379$			11.7976i			0.606002i	0.952990	+	0.303001i	$0.0979886\pi$
$379$			11.7976i			0.606002i	−0.952990	+	0.303001i	$0.902011\pi$
$380$		0			0
$381$	−3.83268	−	2.21280i	−0.196354	−	0.113365i
$382$	−27.7586	−	5.78507i	−1.42025	−	0.295990i
$383$	0.478522	+	0.828825i	0.0244514	+	0.0423510i	0.877992	−	0.478675i	$-0.158883\pi$
$383$	0.478522	+	0.828825i	0.0244514	+	0.0423510i	−0.853541	+	0.521026i	$0.825549\pi$
$384$	−6.22067	−	8.07948i	−0.317447	−	0.412304i
$385$		0			0
$386$	−25.9773	+	8.55483i	−1.32221	+	0.435430i
$387$	−10.9905	+	6.34537i	−0.558679	+	0.322553i
$388$	−9.02330	+	1.02096i	−0.458088	+	0.0518314i
$389$	15.0820	−	26.1228i	0.764689	−	1.32448i	−0.175722	−	0.984440i	$-0.556226\pi$
$389$	15.0820	−	26.1228i	0.764689	−	1.32448i	0.940411	−	0.340041i	$-0.110441\pi$
$390$		0			0
$391$	2.51705			0.127293
$392$	−8.03945	−	18.0933i	−0.406054	−	0.913849i
$393$	14.3073			0.721708
$394$	−1.72697	−	1.54259i	−0.0870037	−	0.0777147i
$395$		0			0
$396$	16.2709	−	1.84101i	0.817645	−	0.0925142i
$397$	5.37540	−	3.10349i	0.269783	−	0.155760i	−0.359006	−	0.933335i	$-0.616884\pi$
$397$	5.37540	−	3.10349i	0.269783	−	0.155760i	0.628789	+	0.777576i	$0.283551\pi$
$398$	−1.05212	+	0.346483i	−0.0527380	+	0.0173676i
$399$	−12.7663	+	7.26317i	−0.639113	+	0.363613i
$400$		0			0
$401$	−13.1565	−	22.7877i	−0.657004	−	1.13796i	−0.981387	−	0.192038i	$-0.938490\pi$
$401$	−13.1565	−	22.7877i	−0.657004	−	1.13796i	0.324384	−	0.945926i	$-0.394843\pi$
$402$	−12.2845	−	2.56017i	−0.612694	−	0.127689i
$403$	−5.32025	−	3.07165i	−0.265020	−	0.153010i
$404$	−7.30571	+	16.7663i	−0.363473	+	0.834153i
$405$		0			0
$406$	−1.59294	−	0.342523i	−0.0790564	−	0.0169991i
$407$			42.2927i			2.09637i
$408$	−0.137886	+	1.48161i	−0.00682637	+	0.0733508i
$409$	−15.9374	−	9.20148i	−0.788055	−	0.454984i	0.0512223	−	0.998687i	$-0.483688\pi$
$409$	−15.9374	−	9.20148i	−0.788055	−	0.454984i	−0.839277	+	0.543703i	$0.817022\pi$
$410$		0			0
$411$	−3.53400	−	6.12107i	−0.174320	−	0.301930i
$412$	−16.4595	+	12.1596i	−0.810902	+	0.599060i
$413$	0.0581707	−	9.18236i	0.00286239	−	0.451834i
$414$	−4.17302	−	12.6716i	−0.205093	−	0.622777i
$415$		0			0
$416$	−6.60762	+	11.9887i	−0.323965	+	0.587795i
$417$	7.84312	−	13.5847i	0.384079	−	0.665245i
$418$	21.7174	−	24.3132i	1.06223	−	1.18920i
$419$	35.2426			1.72171			0.860856	−	0.508848i	$-0.169928\pi$
$419$	35.2426			1.72171			0.860856	+	0.508848i	$0.169928\pi$
$420$		0			0
$421$	−15.6669			−0.763558			−0.381779	−	0.924254i	$-0.624688\pi$
$421$	−15.6669			−0.763558			−0.381779	+	0.924254i	$0.624688\pi$
$422$	8.69128	−	9.73014i	0.423085	−	0.473656i
$423$	12.6630	−	21.9329i	0.615695	−	1.06641i
$424$	3.67917	+	8.00531i	0.178676	+	0.388772i
$425$		0			0
$426$	3.97400	+	12.0673i	0.192541	+	0.584664i
$427$	13.8921	−	23.7136i	0.672285	−	1.14758i
$428$	7.52492	+	10.1859i	0.363731	+	0.492355i
$429$	4.08117	+	7.06879i	0.197041	+	0.341284i
$430$		0			0
$431$	−1.73673	−	1.00270i	−0.0836555	−	0.0482985i	0.457589	−	0.889164i	$-0.348713\pi$
$431$	−1.73673	−	1.00270i	−0.0836555	−	0.0482985i	−0.541244	+	0.840865i	$0.682047\pi$
$432$	18.2294	−	4.17871i	0.877064	−	0.201048i
$433$			13.5978i			0.653469i	0.945116	+	0.326734i	$0.105948\pi$
$433$			13.5978i			0.653469i	−0.945116	+	0.326734i	$0.894052\pi$
$434$	−6.37256	+	7.04393i	−0.305893	+	0.338120i
$435$		0			0
$436$	34.3974	+	14.9883i	1.64734	+	0.717809i
$437$	−23.0022	−	13.2803i	−1.10034	−	0.635283i
$438$	−12.2270	−	2.54818i	−0.584228	−	0.121757i
$439$	−14.5247	−	25.1574i	−0.693224	−	1.20070i	−0.970776	−	0.239989i	$-0.922856\pi$
$439$	−14.5247	−	25.1574i	−0.693224	−	1.20070i	0.277552	−	0.960711i	$-0.410477\pi$
$440$		0			0
$441$	15.3127	+	0.194020i	0.729174	+	0.00923907i
$442$	1.89740	−	0.624849i	0.0902500	−	0.0297211i
$443$	−12.6757	+	7.31831i	−0.602240	+	0.347703i	−0.769922	−	0.638138i	$-0.779705\pi$
$443$	−12.6757	+	7.31831i	−0.602240	+	0.347703i	0.167683	+	0.985841i	$0.446372\pi$
$444$	2.29023	+	20.2411i	0.108689	+	0.960601i
$445$		0			0
$446$	25.5643	+	22.8349i	1.21050	+	1.08126i
$447$	1.48851			0.0704040
$448$	15.9750	+	13.8853i	0.754747	+	0.656016i
$449$	−27.0699			−1.27751			−0.638754	−	0.769411i	$-0.720550\pi$
$449$	−27.0699			−1.27751			−0.638754	+	0.769411i	$0.720550\pi$
$450$		0			0
$451$	−13.7548	+	23.8241i	−0.647689	+	1.12183i
$452$	−0.939568	−	8.30395i	−0.0441936	−	0.390585i
$453$	−5.74168	+	3.31496i	−0.269768	+	0.155750i
$454$	14.2820	−	4.70335i	0.670290	−	0.220739i
$455$		0			0
$456$	9.07725	−	12.8122i	0.425081	−	0.599989i
$457$	−3.80306	−	6.58709i	−0.177900	−	0.308131i	0.763261	−	0.646090i	$-0.223597\pi$
$457$	−3.80306	−	6.58709i	−0.177900	−	0.308131i	−0.941161	+	0.337959i	$0.890264\pi$
$458$	40.8596	+	8.51539i	1.90924	+	0.397898i
$459$	−2.36357	−	1.36461i	−0.110322	−	0.0636943i
$460$		0			0
$461$		−	12.7953i		−	0.595936i	−0.954576	−	0.297968i	$-0.903691\pi$
$461$		−	12.7953i		−	0.595936i	0.954576	−	0.297968i	$-0.0963089\pi$
$462$	12.0121	−	3.87163i	0.558853	−	0.180125i
$463$			27.9178i			1.29745i	0.761024	+	0.648724i	$0.224697\pi$
$463$			27.9178i			1.29745i	−0.761024	+	0.648724i	$0.775303\pi$
$464$	1.69782	−	0.389188i	0.0788191	−	0.0180676i
$465$		0			0
$466$	8.09917	−	38.8624i	0.375187	−	1.80026i
$467$	−11.3054	−	19.5815i	−0.523152	−	0.906126i	−0.999637	−	0.0269432i	$-0.991423\pi$
$467$	−11.3054	−	19.5815i	−0.523152	−	0.906126i	0.476485	−	0.879183i	$-0.341911\pi$
$468$	−6.29138	−	8.51617i	−0.290819	−	0.393660i
$469$	26.0469	+	0.165008i	1.20273	+	0.00761937i
$470$		0			0
$471$	−2.40599	+	1.38910i	−0.110862	+	0.0640062i
$472$	4.09938	+	8.91963i	0.188689	+	0.410559i
$473$	10.8549	−	18.8013i	0.499110	−	0.864484i
$474$	−0.389781	+	0.436371i	−0.0179032	+	0.0200432i
$475$		0			0
$476$	−0.327817	−	3.07130i	−0.0150255	−	0.140773i
$477$	−6.81448			−0.312014
$478$	12.8389	−	14.3735i	0.587239	−	0.657430i
$479$	10.9907	−	19.0365i	0.502180	−	0.869801i	−0.497817	−	0.867282i	$-0.665865\pi$
$479$	10.9907	−	19.0365i	0.502180	−	0.869801i	0.999997	−	0.00251901i	$-0.000801826\pi$
$480$		0			0
$481$	23.6830	−	13.6734i	1.07985	−	0.623453i
$482$	1.86118	+	5.65160i	0.0847744	+	0.257423i
$483$	−5.08471	−	8.93726i	−0.231362	−	0.406659i
$484$	−4.83560	+	3.57234i	−0.219800	+	0.162379i
$485$		0			0
$486$	−4.65802	+	22.3507i	−0.211292	+	1.01385i
$487$	21.9822	+	12.6914i	0.996108	+	0.575103i	0.907095	−	0.420927i	$-0.138295\pi$
$487$	21.9822	+	12.6914i	0.996108	+	0.575103i	0.0890138	+	0.996030i	$0.471628\pi$
$488$	−2.72254	+	29.2543i	−0.123244	+	1.32428i
$489$		−	4.07212i		−	0.184147i
$490$		0			0
$491$		−	36.4635i		−	1.64557i	−0.568350	−	0.822787i	$-0.692418\pi$
$491$		−	36.4635i		−	1.64557i	0.568350	−	0.822787i	$-0.307582\pi$
$492$	−5.29289	+	12.1469i	−0.238622	+	0.547627i
$493$	−0.220133	−	0.127094i	−0.00991429	−	0.00572402i
$494$	−20.6362	−	4.30072i	−0.928467	−	0.193498i
$495$		0			0
$496$	2.98403	−	9.70626i	0.133987	−	0.435824i
$497$	−13.0411	−	22.9220i	−0.584973	−	1.02819i
$498$	3.14460	−	1.03558i	0.140913	−	0.0464053i
$499$	−10.2874	+	5.93945i	−0.460528	+	0.265886i	−0.712266	−	0.701909i	$-0.752331\pi$
$499$	−10.2874	+	5.93945i	−0.460528	+	0.265886i	0.251738	+	0.967795i	$0.418998\pi$
$500$		0			0
$501$	−7.63194	+	13.2189i	−0.340970	+	0.590577i
$502$	19.9158	+	17.7894i	0.888884	+	0.793981i
$503$	17.3055			0.771614			0.385807	−	0.922580i	$-0.373923\pi$
$503$	17.3055			0.771614			0.385807	+	0.922580i	$0.373923\pi$
$504$	−14.9184	+	6.74224i	−0.664520	+	0.300323i
$505$		0			0
$506$	17.0209	+	15.2036i	0.756672	+	0.675884i
$507$	−3.21939	+	5.57615i	−0.142978	+	0.247646i
$508$	−9.75846	+	1.10414i	−0.432962	+	0.0489884i
$509$	−11.8717	+	6.85414i	−0.526205	+	0.303805i	−0.739470	−	0.673190i	$-0.764924\pi$
$509$	−11.8717	+	6.85414i	−0.526205	+	0.303805i	0.213265	+	0.976994i	$0.431590\pi$
$510$		0			0
$511$	25.9250	+	0.164236i	1.14685	+	0.00726537i
$512$	−21.7562	−	6.21824i	−0.961498	−	0.274810i
$513$	14.3997	+	24.9410i	0.635761	+	1.10117i
$514$	35.7671	+	7.45408i	1.57762	+	0.328785i
$515$		0			0
$516$	4.17700	−	9.58603i	0.183882	−	0.422002i
$517$			43.3247i			1.90542i
$518$	−12.9714	−	40.2449i	−0.569930	−	1.76826i
$519$		−	0.119597i		−	0.00524973i
$520$		0			0
$521$	31.4817	+	18.1760i	1.37924	+	0.796304i	0.992068	−	0.125704i	$-0.0401190\pi$
$521$	31.4817	+	18.1760i	1.37924	+	0.796304i	0.387171	+	0.922008i	$0.373452\pi$
$522$	−0.274873	+	1.31893i	−0.0120309	+	0.0577279i
$523$	−2.13211	−	3.69292i	−0.0932306	−	0.161480i	0.815638	−	0.578562i	$-0.196386\pi$
$523$	−2.13211	−	3.69292i	−0.0932306	−	0.161480i	−0.908869	+	0.417082i	$0.863053\pi$
$524$	25.5363	−	18.8651i	1.11556	−	0.824126i
$525$		0			0
$526$	−4.73196	−	14.3689i	−0.206323	−	0.626515i
$527$	−1.28333	+	0.740929i	−0.0559026	+	0.0322754i
$528$	−9.88173	+	9.18614i	−0.430047	+	0.399776i
$529$	−2.20289	+	3.81552i	−0.0957778	+	0.165892i
$530$		0			0
$531$	−7.59279			−0.329499
$532$	−13.2088	+	29.7968i	−0.572675	+	1.29185i
$533$	17.7879			0.770482
$534$	−8.38927	+	9.39203i	−0.363039	+	0.406433i
$535$		0			0
$536$	−25.3016	+	11.6284i	−1.09286	+	0.502270i
$537$	−12.5658	+	7.25487i	−0.542254	+	0.313071i
$538$	3.70038	+	11.2364i	0.159535	+	0.484438i
$539$	−22.8516	+	12.8101i	−0.984288	+	0.551771i
$540$		0			0
$541$	3.34133	+	5.78736i	0.143655	+	0.248818i	0.928870	−	0.370405i	$-0.120781\pi$
$541$	3.34133	+	5.78736i	0.143655	+	0.248818i	−0.785215	+	0.619223i	$0.787448\pi$
$542$	7.82248	−	37.5347i	0.336004	−	1.61225i
$543$	3.11679	+	1.79948i	0.133754	+	0.0772229i
$544$	1.70750	+	2.82626i	0.0732084	+	0.121175i
$545$		0			0
$546$	−6.05158	−	5.47479i	−0.258984	−	0.234300i
$547$		−	45.6888i		−	1.95351i	−0.214353	−	0.976756i	$-0.568764\pi$
$547$		−	45.6888i		−	1.95351i	0.214353	−	0.976756i	$-0.431236\pi$
$548$	−14.3787	−	6.26534i	−0.614226	−	0.267642i
$549$	−19.6805	−	11.3625i	−0.839942	−	0.484941i
$550$		0			0
$551$	1.34113	+	2.32290i	0.0571339	+	0.0989589i
$552$	8.96944	+	6.35469i	0.381765	+	0.270474i
$553$	0.613918	−	1.04795i	0.0261064	−	0.0445633i
$554$	−4.51309	+	1.48625i	−0.191743	+	0.0631445i
$555$		0			0
$556$	−3.91355	−	34.5882i	−0.165972	−	1.46687i
$557$	2.44203	−	4.22972i	0.103472	−	0.179219i	−0.809641	−	0.586926i	$-0.800338\pi$
$557$	2.44203	−	4.22972i	0.103472	−	0.179219i	0.913113	+	0.407707i	$0.133671\pi$
$558$	5.85769	+	5.23229i	0.247976	+	0.221500i
$559$	−14.0378			−0.593734
$560$		0			0
$561$	1.96888			0.0831263
$562$	7.74107	+	6.91459i	0.326538	+	0.291674i
$563$	−1.36792	+	2.36931i	−0.0576509	+	0.0998543i	−0.893410	−	0.449241i	$-0.851694\pi$
$563$	−1.36792	+	2.36931i	−0.0576509	+	0.0998543i	0.835760	+	0.549096i	$0.185028\pi$
$564$	2.34611	+	20.7350i	0.0987891	+	0.873103i
$565$		0			0
$566$	−9.67897	+	3.18747i	−0.406838	+	0.133979i
$567$	0.0393726	−	6.21505i	0.00165349	−	0.261008i
$568$	23.0045	+	16.2983i	0.965248	+	0.683861i
$569$	−2.29674	−	3.97807i	−0.0962843	−	0.166769i	0.813860	−	0.581062i	$-0.197362\pi$
$569$	−2.29674	−	3.97807i	−0.0962843	−	0.166769i	−0.910144	+	0.414292i	$0.864029\pi$
$570$		0			0
$571$	−4.86573	−	2.80923i	−0.203625	−	0.117563i	0.394720	−	0.918801i	$-0.370841\pi$
$571$	−4.86573	−	2.80923i	−0.203625	−	0.117563i	−0.598345	+	0.801239i	$0.704175\pi$
$572$	16.6049	+	7.23539i	0.694286	+	0.302527i
$573$			18.0707i			0.754912i
$574$	5.78185	−	26.8891i	0.241330	−	1.12233i
$575$		0			0
$576$	11.3974	−	13.2817i	0.474892	−	0.553405i
$577$	29.7446	+	17.1731i	1.23828	+	0.714924i	0.968743	−	0.248065i	$-0.0797948\pi$
$577$	29.7446	+	17.1731i	1.23828	+	0.714924i	0.269541	+	0.962989i	$0.413128\pi$
$578$	−4.80673	+	23.0642i	−0.199934	+	0.959345i
$579$	8.71499	+	15.0948i	0.362182	+	0.627318i
$580$		0			0
$581$	−5.97319	+	3.39835i	−0.247810	+	0.140987i
$582$	1.81021	+	5.49684i	0.0750358	+	0.227851i
$583$	10.0956	−	5.82872i	0.418118	−	0.241401i
$584$	−25.1832	+	11.5740i	−1.04209	+	0.478935i
$585$		0			0
$586$	7.98795	−	8.94273i	0.329979	−	0.369421i
$587$	−40.1422			−1.65685			−0.828423	−	0.560103i	$-0.810762\pi$
$587$	−40.1422			−1.65685			−0.828423	+	0.560103i	$0.810762\pi$
$588$	−10.2430	+	7.36833i	−0.422414	+	0.303865i
$589$	15.6369			0.644309
$590$		0			0
$591$	−0.737868	+	1.27802i	−0.0303518	+	0.0525709i
$592$	30.7769	+	33.1074i	1.26492	+	1.36071i
$593$	−9.46884	+	5.46684i	−0.388839	+	0.224496i	−0.681657	−	0.731672i	$-0.738740\pi$
$593$	−9.46884	+	5.46684i	−0.388839	+	0.224496i	0.292818	+	0.956168i	$0.405407\pi$
$594$	−7.74042	−	23.5043i	−0.317593	−	0.964394i
$595$		0			0
$596$	2.65675	−	1.96269i	0.108825	−	0.0803951i
$597$	0.352969	+	0.611361i	0.0144461	+	0.0250213i
$598$	3.01079	−	14.4467i	0.123120	−	0.590771i
$599$	−4.51466	−	2.60654i	−0.184464	−	0.106500i	0.404924	−	0.914350i	$-0.367298\pi$
$599$	−4.51466	−	2.60654i	−0.184464	−	0.106500i	−0.589388	+	0.807850i	$0.700631\pi$
$600$		0			0
$601$			16.1103i			0.657154i	0.944477	+	0.328577i	$0.106569\pi$
$601$			16.1103i			0.657154i	−0.944477	+	0.328577i	$0.893431\pi$
$602$	−4.56287	+	21.2202i	−0.185969	+	0.864869i
$603$		−	21.5379i		−	0.877090i
$604$	−5.87700	+	13.4875i	−0.239132	+	0.548797i
$605$		0			0
$606$	11.4103	+	2.37798i	0.463512	+	0.0965989i
$607$	4.82810	+	8.36252i	0.195967	+	0.339424i	0.947217	−	0.320593i	$-0.103882\pi$
$607$	4.82810	+	8.36252i	0.195967	+	0.339424i	−0.751250	+	0.660017i	$0.770549\pi$
$608$	−0.692317	−	34.8368i	−0.0280772	−	1.41282i
$609$	−0.00657809	+	1.03837i	−0.000266558	+	0.0420767i
$610$		0			0
$611$	24.2609	−	14.0070i	0.981491	−	0.566664i
$612$	−2.53781	+	0.287146i	−0.102585	+	0.0116072i
$613$	3.92388	−	6.79635i	0.158484	−	0.274502i	−0.775838	−	0.630932i	$-0.782673\pi$
$613$	3.92388	−	6.79635i	0.158484	−	0.274502i	0.934322	+	0.356430i	$0.116006\pi$
$614$	10.9976	+	9.82343i	0.443827	+	0.396441i
$615$		0			0
$616$	16.3347	−	22.7490i	0.658143	−	0.916582i
$617$	28.8434			1.16119			0.580597	−	0.814191i	$-0.302819\pi$
$617$	28.8434			1.16119			0.580597	+	0.814191i	$0.302819\pi$
$618$	9.72643	+	8.68797i	0.391254	+	0.349481i
$619$	−1.24278	+	2.15256i	−0.0499517	+	0.0865189i	−0.889920	−	0.456116i	$-0.849240\pi$
$619$	−1.24278	+	2.15256i	−0.0499517	+	0.0865189i	0.839968	+	0.542635i	$0.182573\pi$
$620$		0			0
$621$	−17.4604	+	10.0807i	−0.700660	+	0.404526i
$622$	10.6465	−	3.50609i	0.426885	−	0.140581i
$623$	13.2134	−	22.5550i	0.529383	−	0.903649i
$624$	8.33885	+	2.56364i	0.333821	+	0.102628i
$625$		0			0
$626$	20.0286	+	4.17409i	0.800504	+	0.166830i
$627$	−17.9927	−	10.3881i	−0.718558	−	0.414860i
$628$	−2.46269	+	5.65177i	−0.0982722	+	0.225530i
$629$		−	6.59647i		−	0.263019i
$630$		0			0
$631$			8.90728i			0.354593i	0.984157	+	0.177297i	$0.0567352\pi$
$631$			8.90728i			0.354593i	−0.984157	+	0.177297i	$0.943265\pi$
$632$	−0.120314	+	1.29280i	−0.00478585	+	0.0514250i
$633$	−7.20066	−	4.15730i	−0.286200	−	0.165238i
$634$	1.02055	−	4.89694i	0.0405314	−	0.194482i
$635$		0			0
$636$	4.51609	−	3.33630i	0.179075	−	0.132293i
$637$	14.5614	+	8.65485i	0.576944	+	0.342917i
$638$	−0.720911	−	2.18910i	−0.0285412	−	0.0866672i
$639$	−18.8848	+	10.9032i	−0.747073	+	0.431323i
$640$		0			0
$641$	−7.31652	+	12.6726i	−0.288985	+	0.500537i	−0.973568	−	0.228398i	$-0.926651\pi$
$641$	−7.31652	+	12.6726i	−0.288985	+	0.500537i	0.684583	+	0.728935i	$0.259984\pi$
$642$	5.37653	−	6.01917i	0.212195	−	0.237558i
$643$	24.2513			0.956380			0.478190	−	0.878256i	$-0.341293\pi$
$643$	24.2513			0.956380			0.478190	+	0.878256i	$0.341293\pi$
$644$	−20.8598	−	9.24707i	−0.821990	−	0.364386i
$645$		0			0
$646$	−3.38730	+	3.79218i	−0.133272	+	0.149201i
$647$	14.9578	−	25.9077i	0.588053	−	1.01854i	−0.406435	−	0.913680i	$-0.633228\pi$
$647$	14.9578	−	25.9077i	0.588053	−	1.01854i	0.994487	−	0.104857i	$-0.0334386\pi$
$648$	2.77465	+	6.03722i	0.108999	+	0.237164i
$649$	11.2487	−	6.49444i	0.441550	−	0.254929i
$650$		0			0
$651$	5.22326	+	3.05993i	0.204716	+	0.119928i
$652$	−5.36935	−	7.26808i	−0.210280	−	0.284640i
$653$	−7.78155	−	13.4780i	−0.304516	−	0.527436i	0.672638	−	0.739972i	$-0.265161\pi$
$653$	−7.78155	−	13.4780i	−0.304516	−	0.527436i	−0.977153	+	0.212535i	$0.931828\pi$
$654$	4.87863	−	23.4092i	0.190770	−	0.915373i
$655$		0			0
$656$	6.56957	+	28.6594i	0.256498	+	1.11896i
$657$		−	21.4371i		−	0.836340i
$658$	−13.2879	−	41.2269i	−0.518016	−	1.60719i
$659$		−	30.2702i		−	1.17916i	−0.807710	−	0.589580i	$-0.799293\pi$
$659$		−	30.2702i		−	1.17916i	0.807710	−	0.589580i	$-0.200707\pi$
$660$		0			0
$661$	15.5209	+	8.96099i	0.603693	+	0.348542i	0.770493	−	0.637449i	$-0.220010\pi$
$661$	15.5209	+	8.96099i	0.603693	+	0.348542i	−0.166800	+	0.985991i	$0.553344\pi$
$662$	32.5761	+	6.78907i	1.26611	+	0.263865i
$663$	−0.636547	−	1.10253i	−0.0247214	−	0.0428188i
$664$	4.24714	−	5.99470i	0.164821	−	0.232640i
$665$		0			0
$666$	−33.2087	+	10.9363i	−1.28681	+	0.423772i
$667$	−1.62619	+	0.938880i	−0.0629662	+	0.0363536i
$668$	3.80818	+	33.6569i	0.147343	+	1.30222i
$669$	10.9226	−	18.9185i	0.422292	−	0.731432i
$670$		0			0
$671$	38.8754			1.50077
$672$	6.58581	−	11.7721i	0.254053	−	0.454119i
$673$	−21.1876			−0.816723			−0.408362	−	0.912820i	$-0.633900\pi$
$673$	−21.1876			−0.816723			−0.408362	+	0.912820i	$0.633900\pi$
$674$	5.37966	+	4.80529i	0.207217	+	0.185093i
$675$		0			0
$676$	1.60641	+	14.1975i	0.0617850	+	0.546059i
$677$	21.8732	−	12.6285i	0.840657	−	0.485353i	−0.0168308	−	0.999858i	$-0.505358\pi$
$677$	21.8732	−	12.6285i	0.840657	−	0.485353i	0.857487	+	0.514505i	$0.172024\pi$
$678$	−5.05863	+	1.66590i	−0.194275	+	0.0639786i
$679$	−5.94041	−	10.4413i	−0.227972	−	0.400700i
$680$		0			0
$681$	−4.79140	−	8.29895i	−0.183607	−	0.318016i
$682$	−13.1536	−	2.74128i	−0.503676	−	0.104969i
$683$	−19.1391	−	11.0499i	−0.732336	−	0.422814i	0.0869404	−	0.996214i	$-0.472291\pi$
$683$	−19.1391	−	11.0499i	−0.732336	−	0.422814i	−0.819276	+	0.573399i	$0.805624\pi$
$684$	24.7068	+	10.7657i	0.944689	+	0.411637i
$685$		0			0
$686$	17.8162	−	19.1985i	0.680225	−	0.733004i
$687$		−	26.5993i		−	1.01483i
$688$	−5.18452	−	22.6172i	−0.197658	−	0.862273i
$689$	−6.52791	−	3.76889i	−0.248694	−	0.143583i
$690$		0			0
$691$	9.05508	+	15.6839i	0.344471	+	0.596642i	0.985258	−	0.171077i	$-0.0547248\pi$
$691$	9.05508	+	15.6839i	0.344471	+	0.596642i	−0.640786	+	0.767719i	$0.721391\pi$
$692$	−0.157697	−	0.213462i	−0.00599473	−	0.00811461i
$693$	10.7118	+	18.8279i	0.406908	+	0.715212i
$694$	−0.737153	−	2.23841i	−0.0279819	−	0.0849691i
$695$		0			0
$696$	−0.463569	−	1.00865i	−0.0175715	−	0.0382330i
$697$	2.14537	−	3.71588i	0.0812615	−	0.140749i
$698$	26.0098	−	29.1187i	0.984486	−	1.10216i
$699$	−25.2991			−0.956901
$700$		0			0
$701$	14.4315			0.545070			0.272535	−	0.962146i	$-0.412138\pi$
$701$	14.4315			0.545070			0.272535	+	0.962146i	$0.412138\pi$
$702$	−10.6594	+	11.9335i	−0.402313	+	0.450401i
$703$	−34.8038	+	60.2820i	−1.31265	+	2.27358i
$704$	−5.52481	+	29.4255i	−0.208224	+	1.10902i
$705$		0			0
$706$	12.0134	+	36.4796i	0.452131	+	1.37293i
$707$	−24.1934	−	0.153266i	−0.909885	−	0.00576416i
$708$	5.03189	−	3.71735i	0.189110	−	0.139706i
$709$	18.5131	+	32.0657i	0.695275	+	1.20425i	0.970088	+	0.242753i	$0.0780505\pi$
$709$	18.5131	+	32.0657i	0.695275	+	1.20425i	−0.274814	+	0.961498i	$0.588616\pi$
$710$		0			0
$711$	−0.869718	−	0.502132i	−0.0326170	−	0.0188314i
$712$	−2.58953	+	27.8251i	−0.0970469	+	1.04279i
$713$			10.9469i			0.409965i
$714$	−1.87355	+	0.603866i	−0.0701157	+	0.0225991i
$715$		0			0
$716$	−12.8620	+	29.5176i	−0.480674	+	1.10312i
$717$	−10.6369	−	6.14124i	−0.397244	−	0.229349i
$718$	−23.1967	−	4.83433i	−0.865692	−	0.180416i
$719$	−10.0975	−	17.4894i	−0.376573	−	0.652243i	0.613988	−	0.789315i	$-0.289564\pi$
$719$	−10.0975	−	17.4894i	−0.376573	−	0.652243i	−0.990561	+	0.137072i	$0.956231\pi$
$720$		0			0
$721$	−23.3581	−	13.6838i	−0.869902	−	0.509613i
$722$	25.4412	−	8.37828i	0.946824	−	0.311807i
$723$	3.28401	−	1.89602i	0.122134	−	0.0705138i
$724$	7.93570	−	0.897902i	0.294928	−	0.0333703i
$725$		0			0
$726$	2.85750	+	2.55242i	0.106052	+	0.0947292i
$727$	−10.7925			−0.400272			−0.200136	−	0.979768i	$-0.564138\pi$
$727$	−10.7925			−0.400272			−0.200136	+	0.979768i	$0.564138\pi$
$728$	−18.0200	−	1.79224i	−0.667865	−	0.0664248i
$729$	7.50278			0.277881
$730$		0			0
$731$	−1.69306	+	2.93247i	−0.0626202	+	0.108461i
$732$	18.6056	−	2.10517i	0.687683	−	0.0778094i
$733$	−6.26329	+	3.61611i	−0.231340	+	0.133564i	−0.611190	−	0.791484i	$-0.709309\pi$
$733$	−6.26329	+	3.61611i	−0.231340	+	0.133564i	0.379850	+	0.925048i	$0.375976\pi$
$734$	11.3427	−	3.73538i	0.418668	−	0.137875i
$735$		0			0
$736$	24.3881	−	0.484669i	0.898958	−	0.0178651i
$737$	18.4223	+	31.9083i	0.678593	+	1.17536i
$738$	−22.2637	−	4.63990i	−0.819539	−	0.170797i
$739$	1.71927	+	0.992622i	0.0632444	+	0.0365142i	0.531289	−	0.847191i	$-0.321708\pi$
$739$	1.71927	+	0.992622i	0.0632444	+	0.0365142i	−0.468044	+	0.883705i	$0.655041\pi$
$740$		0			0
$741$			13.4340i			0.493511i
$742$	−7.81909	+	8.64286i	−0.287048	+	0.317289i
$743$		−	19.8225i		−	0.727216i	−0.931552	−	0.363608i	$-0.881545\pi$
$743$		−	19.8225i		−	0.727216i	0.931552	−	0.363608i	$-0.118455\pi$
$744$	−6.44368	−	0.599680i	−0.236237	−	0.0219853i
$745$		0			0
$746$	−2.99416	+	14.3669i	−0.109624	+	0.526011i
$747$	2.84124	+	4.92116i	0.103955	+	0.180056i
$748$	3.51414	−	2.59610i	0.128490	−	0.0949228i
$749$	−8.46821	+	14.4551i	−0.309421	+	0.528178i
$750$		0			0
$751$	−20.8718	+	12.0504i	−0.761624	+	0.439724i	−0.829879	−	0.557944i	$-0.811590\pi$
$751$	−20.8718	+	12.0504i	−0.761624	+	0.439724i	0.0682545	+	0.997668i	$0.478257\pi$
$752$	31.5279	+	33.9153i	1.14971	+	1.23676i
$753$	8.50921	−	14.7384i	0.310093	−	0.537097i
$754$	−0.992774	+	1.11144i	−0.0361547	+	0.0404762i
$755$		0			0
$756$	14.5745	+	19.9922i	0.530070	+	0.727109i
$757$	−34.8711			−1.26741			−0.633706	−	0.773574i	$-0.718467\pi$
$757$	−34.8711			−1.26741			−0.633706	+	0.773574i	$0.718467\pi$
$758$	11.1146	−	12.4431i	0.403702	−	0.451955i
$759$	7.27236	−	12.5961i	0.263970	−	0.457209i
$760$		0			0
$761$	7.76620	−	4.48382i	0.281524	−	0.162538i	−0.352589	−	0.935778i	$-0.614699\pi$
$761$	7.76620	−	4.48382i	0.281524	−	0.162538i	0.634113	+	0.773240i	$0.281365\pi$
$762$	1.95770	+	5.94469i	0.0709200	+	0.215353i
$763$	−0.314438	+	49.6347i	−0.0113834	+	1.79690i
$764$	23.8273	+	32.2533i	0.862043	+	1.16688i
$765$		0			0
$766$	0.276138	−	1.32500i	0.00997727	−	0.0478741i
$767$	−7.27349	−	4.19935i	−0.262631	−	0.151630i
$768$	−1.05071	+	14.3821i	−0.0379141	+	0.518970i
$769$			0.573577i			0.0206837i	0.999947	+	0.0103419i	$0.00329197\pi$
$769$			0.573577i			0.0206837i	−0.999947	+	0.0103419i	$0.996708\pi$
$770$		0			0
$771$		−	23.2841i		−	0.838556i
$772$	35.4584	+	15.4506i	1.27617	+	0.556078i
$773$	3.76591	+	2.17425i	0.135450	+	0.0782023i	0.566194	−	0.824272i	$-0.308415\pi$
$773$	3.76591	+	2.17425i	0.135450	+	0.0782023i	−0.430744	+	0.902474i	$0.641749\pi$
$774$	17.5699	+	3.66168i	0.631537	+	0.131616i
$775$		0			0
$776$	10.4789	+	7.42411i	0.376170	+	0.266510i
$777$	−23.4220	+	13.3256i	−0.840259	+	0.478052i
$778$	−40.5179	+	13.3433i	−1.45264	+	0.478381i
$779$	−39.2109	+	22.6384i	−1.40488	+	0.811107i
$780$		0			0
$781$	18.6519	−	32.3060i	0.667417	−	1.15600i
$782$	−2.65478	−	2.37134i	−0.0949348	−	0.0847990i
$783$	2.03603			0.0727618
$784$	−8.56651	+	26.6574i	−0.305947	+	0.952049i
$785$		0			0
$786$	−15.0902	−	13.4790i	−0.538249	−	0.480782i
$787$	10.5248	−	18.2295i	0.375168	−	0.649811i	−0.615184	−	0.788384i	$-0.710918\pi$
$787$	10.5248	−	18.2295i	0.375168	−	0.649811i	0.990352	+	0.138573i	$0.0442516\pi$
$788$	0.368181	+	3.25400i	0.0131159	+	0.115919i
$789$	−8.34944	+	4.82055i	−0.297248	+	0.171616i
$790$		0			0
$791$	9.60890	−	5.46683i	0.341653	−	0.194378i
$792$	−18.8957	−	13.3873i	−0.671428	−	0.475695i
$793$	−12.5686	−	21.7694i	−0.446323	−	0.773054i
$794$	−8.59335	−	1.79091i	−0.304967	−	0.0635570i
$795$		0			0
$796$	1.43611	+	0.625770i	0.0509017	+	0.0221798i
$797$		−	14.7349i		−	0.521938i	−0.965347	−	0.260969i	$-0.915958\pi$
$797$		−	14.7349i		−	0.521938i	0.965347	−	0.260969i	$-0.0840420\pi$
$798$	20.3075	+	4.36663i	0.718879	+	0.154577i
$799$		−	6.75744i		−	0.239061i
$800$		0			0
$801$	−18.7190	−	10.8074i	−0.661403	−	0.381861i
$802$	−7.59213	+	36.4295i	−0.268087	+	1.28637i
$803$	18.3360	+	31.7590i	0.647065	+	1.12075i
$804$	10.5447	+	14.2736i	0.371883	+	0.503390i
$805$		0			0
$806$	2.71753	+	8.25198i	0.0957210	+	0.290663i
$807$	6.52923	−	3.76965i	0.229840	−	0.132698i
$808$	23.5011	−	10.8009i	0.826767	−	0.379975i
$809$	7.23808	−	12.5367i	0.254477	−	0.440768i	−0.710276	−	0.703923i	$-0.751430\pi$
$809$	7.23808	−	12.5367i	0.254477	−	0.440768i	0.964753	+	0.263156i	$0.0847632\pi$
$810$		0			0
$811$	−18.5825			−0.652521			−0.326260	−	0.945280i	$-0.605789\pi$
$811$	−18.5825			−0.652521			−0.326260	+	0.945280i	$0.605789\pi$
$812$	1.35741	+	1.86199i	0.0476358	+	0.0653431i
$813$	−24.4348			−0.856967
$814$	39.8444	−	44.6069i	1.39654	−	1.56347i
$815$		0			0
$816$	1.54127	−	1.43278i	0.0539553	−	0.0501573i
$817$	30.9442	−	17.8656i	1.08260	−	0.625040i
$818$	8.14069	+	24.7198i	0.284633	+	0.864306i
$819$	7.08003	−	12.0855i	0.247396	−	0.422302i
$820$		0			0
$821$	8.20275	+	14.2076i	0.286278	+	0.495848i	0.972918	−	0.231149i	$-0.0742486\pi$
$821$	8.20275	+	14.2076i	0.286278	+	0.495848i	−0.686640	+	0.726997i	$0.740915\pi$
$822$	−2.03934	+	9.78542i	−0.0711303	+	0.341306i
$823$	38.0161	+	21.9486i	1.32516	+	0.765081i	0.984547	−	0.175123i	$-0.0560323\pi$
$823$	38.0161	+	21.9486i	1.32516	+	0.765081i	0.340612	+	0.940204i	$0.389366\pi$
$824$	28.8158	+	2.68173i	1.00385	+	0.0934226i
$825$		0			0
$826$	−8.71214	+	9.63000i	−0.303134	+	0.335070i
$827$			8.10796i			0.281941i	0.990014	+	0.140971i	$0.0450224\pi$
$827$			8.10796i			0.281941i	−0.990014	+	0.140971i	$0.954978\pi$
$828$	−7.53673	+	17.2964i	−0.261919	+	0.601093i
$829$	−36.5657	−	21.1112i	−1.26998	−	0.733223i	−0.294995	−	0.955499i	$-0.595318\pi$
$829$	−36.5657	−	21.1112i	−1.26998	−	0.733223i	−0.974984	+	0.222276i	$0.928651\pi$
$830$		0			0
$831$	1.51407	+	2.62245i	0.0525225	+	0.0909716i
$832$	18.2639	−	6.41961i	0.633185	−	0.222560i
$833$	3.56421	−	1.99802i	0.123492	−	0.0692273i
$834$	−21.0705	+	6.93893i	−0.729613	+	0.240275i
$835$		0			0
$836$	−45.8114	+	5.18343i	−1.58442	+	0.179273i
$837$	5.93481	−	10.2794i	0.205137	−	0.355308i
$838$	−37.1710	−	33.2024i	−1.28405	−	1.14696i
$839$	−31.8404			−1.09925			−0.549627	−	0.835410i	$-0.685230\pi$
$839$	−31.8404			−1.09925			−0.549627	+	0.835410i	$0.685230\pi$
$840$		0			0
$841$	−28.8104			−0.993461
$842$	16.5242	+	14.7599i	0.569460	+	0.508661i
$843$	3.30745	−	5.72868i	0.113915	−	0.197306i
$844$	−18.3337	+	2.07441i	−0.631072	+	0.0714040i
$845$		0			0
$846$	−34.0191	+	11.2031i	−1.16960	+	0.385171i
$847$	−6.86233	−	4.02014i	−0.235792	−	0.138134i
$848$	3.66139	−	11.9095i	0.125733	−	0.408975i
$849$	3.24714	+	5.62422i	0.111442	+	0.193023i
$850$		0			0
$851$	−42.2015	−	24.3650i	−1.44665	−	0.835223i
$852$	7.17729	−	16.4716i	0.245890	−	0.564306i
$853$			16.2023i			0.554755i	0.960761	+	0.277378i	$0.0894653\pi$
$853$			16.2023i			0.554755i	−0.960761	+	0.277378i	$0.910535\pi$
$854$	−36.9930	+	11.9233i	−1.26587	+	0.408006i
$855$		0			0
$856$	1.65958	−	17.8326i	0.0567234	−	0.609505i
$857$	−35.4659	−	20.4762i	−1.21149	−	0.699455i	−0.248407	−	0.968656i	$-0.579907\pi$
$857$	−35.4659	−	20.4762i	−1.21149	−	0.699455i	−0.963084	+	0.269201i	$0.913240\pi$
$858$	2.35509	−	11.3005i	0.0804015	−	0.385792i
$859$	−6.02640	−	10.4380i	−0.205618	−	0.356141i	0.744711	−	0.667387i	$-0.232587\pi$
$859$	−6.02640	−	10.4380i	−0.205618	−	0.356141i	−0.950329	+	0.311246i	$0.899254\pi$
$860$		0			0
$861$	−17.5278	−	0.111039i	−0.597345	−	0.00378421i
$862$	0.887107	+	2.69376i	0.0302150	+	0.0917499i
$863$	0.494372	−	0.285426i	0.0168286	−	0.00971602i	−0.491562	−	0.870843i	$-0.663574\pi$
$863$	0.494372	−	0.285426i	0.0168286	−	0.00971602i	0.508391	+	0.861127i	$0.330241\pi$
$864$	−23.1637	−	12.7668i	−0.788045	−	0.434334i
$865$		0			0
$866$	12.8106	−	14.3418i	0.435323	−	0.487356i
$867$	15.0146			0.509924
$868$	13.3574	−	1.42571i	0.453380	−	0.0483918i
$869$	1.71798			0.0582784
$870$		0			0
$871$	11.9120	−	20.6321i	0.403622	−	0.699093i
$872$	−22.1590	−	48.2146i	−0.750398	−	1.63275i
$873$	−8.60232	+	4.96655i	−0.291144	+	0.168092i
$874$	11.7493	+	35.6775i	0.397426	+	1.20681i
$875$		0			0
$876$	10.4954	+	14.2068i	0.354605	+	0.480003i
$877$	9.47193	+	16.4059i	0.319844	+	0.553987i	0.980455	−	0.196742i	$-0.0630361\pi$
$877$	9.47193	+	16.4059i	0.319844	+	0.553987i	−0.660611	+	0.750728i	$0.729703\pi$
$878$	−8.38165	+	40.2178i	−0.282867	+	1.35729i
$879$	−6.61794	−	3.82087i	−0.223218	−	0.128875i
$880$		0			0
$881$		−	35.7695i		−	1.20511i	−0.798079	−	0.602553i	$-0.794150\pi$
$881$		−	35.7695i		−	1.20511i	0.798079	−	0.602553i	$-0.205850\pi$
$882$	−15.9677	−	14.6308i	−0.537662	−	0.492646i
$883$		−	25.4594i		−	0.856776i	−0.903595	−	0.428388i	$-0.859082\pi$
$883$		−	25.4594i		−	0.856776i	0.903595	−	0.428388i	$-0.140918\pi$
$884$	−2.58990	−	1.12852i	−0.0871076	−	0.0379561i
$885$		0			0
$886$	20.2639	+	4.22313i	0.680779	+	0.141879i
$887$	5.30243	+	9.18408i	0.178038	+	0.308371i	0.941209	−	0.337826i	$-0.109692\pi$
$887$	5.30243	+	9.18408i	0.178038	+	0.308371i	−0.763170	+	0.646197i	$0.776358\pi$
$888$	16.6538	−	23.5063i	0.558865	−	0.788821i
$889$	−6.42439	−	11.2920i	−0.215467	−	0.378721i
$890$		0			0
$891$	7.61364	−	4.39574i	0.255067	−	0.147263i
$892$	−5.45015	−	48.1687i	−0.182485	−	1.61281i
$893$	−35.6531	+	61.7530i	−1.19309	+	2.06648i
$894$	−1.56996	−	1.40234i	−0.0525072	−	0.0469012i
$895$		0			0
$896$	−3.76766	−	29.6952i	−0.125869	−	0.992047i
$897$	−9.40472			−0.314014
$898$	28.5511	+	25.5028i	0.952763	+	0.851040i
$899$	0.552744	−	0.957381i	0.0184350	−	0.0319304i
$900$		0			0
$901$	−1.57463	+	0.909116i	−0.0524587	+	0.0302870i
$902$	36.9523	−	12.1691i	1.23038	−	0.405187i
$903$	13.8324	+	0.0876291i	0.460315	+	0.00291611i
$904$	−6.83225	+	9.64350i	−0.227237	+	0.320738i
$905$		0			0
$906$	9.17891	+	1.91294i	0.304949	+	0.0635533i
$907$	−13.3054	−	7.68190i	−0.441800	−	0.255073i	0.262561	−	0.964915i	$-0.415433\pi$
$907$	−13.3054	−	7.68190i	−0.441800	−	0.255073i	−0.704361	+	0.709842i	$0.748766\pi$
$908$	−19.4946	−	8.49454i	−0.646951	−	0.281901i
$909$			20.0052i			0.663531i
$910$		0			0
$911$			22.0734i			0.731324i	0.930748	+	0.365662i	$0.119157\pi$
$911$			22.0734i			0.731324i	−0.930748	+	0.365662i	$0.880843\pi$
$912$	−21.6445	+	4.96154i	−0.716720	+	0.164293i
$913$	−8.41856	−	4.86046i	−0.278614	−	0.160858i
$914$	−2.19461	+	10.5304i	−0.0725911	+	0.348315i
$915$		0			0
$916$	−35.0729	−	47.4755i	−1.15884	−	1.56864i
$917$	36.2392	+	21.2299i	1.19672	+	0.701074i
$918$	1.20729	+	3.66601i	0.0398464	+	0.120996i
$919$	45.1598	−	26.0730i	1.48968	−	0.860069i	0.489753	−	0.871861i	$-0.337087\pi$
$919$	45.1598	−	26.0730i	1.48968	−	0.860069i	0.999930	+	0.0117923i	$0.00375369\pi$
$920$		0			0
$921$	4.69884	−	8.13863i	0.154832	−	0.268177i
$922$	−12.0546	+	13.4954i	−0.396996	+	0.444448i
$923$	−24.1209			−0.793949
$924$	−16.3169	−	7.23322i	−0.536785	−	0.237955i
$925$		0			0
$926$	26.3016	−	29.4454i	0.864323	−	0.967634i
$927$	−11.1922	+	19.3855i	−0.367600	+	0.636702i
$928$	−2.15737	−	1.18904i	−0.0708193	−	0.0390323i
$929$	24.8707	−	14.3591i	0.815982	−	0.471107i	−0.0330469	−	0.999454i	$-0.510521\pi$
$929$	24.8707	−	14.3591i	0.815982	−	0.471107i	0.849029	+	0.528346i	$0.177188\pi$
$930$		0			0
$931$	−43.1134	−	0.546272i	−1.41298	−	0.0179033i
$932$	−45.1549	+	33.3585i	−1.47910	+	1.09270i
$933$	−3.57173	−	6.18641i	−0.116933	−	0.202534i
$934$	−6.52394	+	31.3039i	−0.213470	+	1.02430i
$935$		0			0
$936$	−1.38753	+	14.9093i	−0.0453529	+	0.487326i
$937$		−	44.9045i		−	1.46697i	−0.679707	−	0.733484i	$-0.737893\pi$
$937$		−	44.9045i		−	1.46697i	0.679707	−	0.733484i	$-0.262107\pi$
$938$	−27.3167	−	24.7131i	−0.891921	−	0.806910i
$939$		−	13.0385i		−	0.425495i
$940$		0			0
$941$	15.3727	+	8.87541i	0.501134	+	0.289330i	0.729182	−	0.684320i	$-0.239901\pi$
$941$	15.3727	+	8.87541i	0.501134	+	0.289330i	−0.228048	+	0.973650i	$0.573234\pi$
$942$	3.84632	+	0.801598i	0.125320	+	0.0261175i
$943$	−15.8484	−	27.4503i	−0.516096	−	0.893905i
$944$	4.07957	−	13.2698i	0.132779	−	0.431894i
$945$		0			0
$946$	−29.1618	+	9.60352i	−0.948130	+	0.312237i
$947$	−32.1100	+	18.5387i	−1.04344	+	0.602428i	−0.920804	−	0.390025i	$-0.872467\pi$
$947$	−32.1100	+	18.5387i	−1.04344	+	0.602428i	−0.122631	+	0.992452i	$0.539133\pi$
$948$	0.822218	−	0.0930316i	0.0267044	−	0.00302153i
$949$	11.8562	−	20.5356i	0.384869	−	0.666613i
$950$		0			0
$951$	−3.18787			−0.103374
$952$	−2.54775	+	3.54820i	−0.0825730	+	0.114998i
$953$	28.5420			0.924567			0.462283	−	0.886732i	$-0.347030\pi$
$953$	28.5420			0.924567			0.462283	+	0.886732i	$0.347030\pi$
$954$	7.18736	+	6.41999i	0.232699	+	0.207855i
$955$		0			0
$956$	−27.0829	+	3.06435i	−0.875923	+	0.0991082i
$957$	−1.27203	+	0.734408i	−0.0411189	+	0.0237400i
$958$	−29.5266	+	9.72368i	−0.953962	+	0.314158i
$959$	0.131440	−	20.7481i	0.00424442	−	0.669991i
$960$		0			0
$961$	12.2776	+	21.2655i	0.396052	+	0.685983i
$962$	−37.8607	−	7.89042i	−1.22068	−	0.254397i
$963$	11.9966	+	6.92626i	0.386586	+	0.223196i
$964$	3.36141	−	7.71428i	0.108264	−	0.248460i
$965$		0			0
$966$	−3.05694	+	14.2166i	−0.0983554	+	0.457413i
$967$		−	5.33936i		−	0.171702i	−0.996308	−	0.0858510i	$-0.972639\pi$
$967$		−	5.33936i		−	0.171702i	0.996308	−	0.0858510i	$-0.0273609\pi$
$968$	8.46573	+	0.787860i	0.272099	+	0.0253228i
$969$	2.80635	+	1.62025i	0.0901530	+	0.0520498i
$970$		0			0
$971$	−5.49906	−	9.52465i	−0.176473	−	0.305660i	0.764197	−	0.644983i	$-0.223136\pi$
$971$	−5.49906	−	9.52465i	−0.176473	−	0.305660i	−0.940670	+	0.339323i	$0.889802\pi$
$972$	25.9697	−	19.1853i	0.832978	−	0.615368i
$973$	40.0236	−	22.7708i	1.28310	−	0.729999i
$974$	−11.2283	−	34.0955i	−0.359778	−	1.09249i
$975$		0			0
$976$	30.4323	−	28.2901i	0.974113	−	0.905544i
$977$	−15.7434	+	27.2684i	−0.503676	+	0.872392i	0.496315	+	0.868142i	$0.334686\pi$
$977$	−15.7434	+	27.2684i	−0.503676	+	0.872392i	−0.999991	+	0.00424979i	$0.998647\pi$
$978$	−3.83638	+	4.29493i	−0.122674	+	0.137337i
$979$	36.9761			1.18176
$980$		0			0
$981$	41.0424			1.31038
$982$	−34.3526	+	38.4587i	−1.09624	+	1.22727i
$983$	17.2762	−	29.9232i	0.551025	−	0.954402i	−0.447176	−	0.894446i	$-0.647570\pi$
$983$	17.2762	−	29.9232i	0.551025	−	0.954402i	0.998201	−	0.0599567i	$-0.0190963\pi$
$984$	17.0263	−	7.82512i	0.542777	−	0.249456i
$985$		0			0
$986$	0.112442	+	0.341438i	0.00358088	+	0.0108736i
$987$	−23.9935	+	13.6507i	−0.763722	+	0.434507i
$988$	17.7136	+	23.9776i	0.563545	+	0.762829i
$989$	12.5072	+	21.6630i	0.397704	+	0.688844i
$990$		0			0
$991$	47.8668	+	27.6359i	1.52054	+	0.877884i	0.999707	+	0.0242247i	$0.00771173\pi$
$991$	47.8668	+	27.6359i	1.52054	+	0.877884i	0.520833	+	0.853659i	$0.325622\pi$
$992$	−12.2917	+	7.42608i	−0.390261	+	0.235778i
$993$		−	21.2068i		−	0.672978i
$994$	−7.84033	+	36.4623i	−0.248680	+	1.15652i
$995$		0			0
$996$	−4.29229	−	1.87032i	−0.136007	−	0.0592632i
$997$	−13.2344	−	7.64087i	−0.419137	−	0.241989i	0.275571	−	0.961281i	$-0.411133\pi$
$997$	−13.2344	−	7.64087i	−0.419137	−	0.241989i	−0.694708	+	0.719292i	$0.744466\pi$
$998$	16.4459	+	3.42744i	0.520587	+	0.108494i
$999$	26.4187	+	45.7586i	0.835851	+	1.44774i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.p.c.451.4		32
4.3	odd	2	inner	700.2.p.c.451.8		32
5.2	odd	4		700.2.t.d.199.11		32
5.3	odd	4		700.2.t.c.199.6		32
5.4	even	2		140.2.o.a.31.13	yes	32
7.5	odd	6	inner	700.2.p.c.551.8		32
20.3	even	4		700.2.t.c.199.1		32
20.7	even	4		700.2.t.d.199.16		32
20.19	odd	2		140.2.o.a.31.9	✓	32
28.19	even	6	inner	700.2.p.c.551.4		32
35.4	even	6		980.2.g.a.391.7		32
35.9	even	6		980.2.o.f.411.9		32
35.12	even	12		700.2.t.c.299.1		32
35.19	odd	6		140.2.o.a.131.9	yes	32
35.24	odd	6		980.2.g.a.391.8		32
35.33	even	12		700.2.t.d.299.16		32
35.34	odd	2		980.2.o.f.31.13		32
140.19	even	6		140.2.o.a.131.13	yes	32
140.39	odd	6		980.2.g.a.391.6		32
140.47	odd	12		700.2.t.c.299.6		32
140.59	even	6		980.2.g.a.391.5		32
140.79	odd	6		980.2.o.f.411.13		32
140.103	odd	12		700.2.t.d.299.11		32
140.139	even	2		980.2.o.f.31.9		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.9	✓	32	20.19	odd	2
140.2.o.a.31.13	yes	32	5.4	even	2
140.2.o.a.131.9	yes	32	35.19	odd	6
140.2.o.a.131.13	yes	32	140.19	even	6
700.2.p.c.451.4		32	1.1	even	1	trivial
700.2.p.c.451.8		32	4.3	odd	2	inner
700.2.p.c.551.4		32	28.19	even	6	inner
700.2.p.c.551.8		32	7.5	odd	6	inner
700.2.t.c.199.1		32	20.3	even	4
700.2.t.c.199.6		32	5.3	odd	4
700.2.t.c.299.1		32	35.12	even	12
700.2.t.c.299.6		32	140.47	odd	12
700.2.t.d.199.11		32	5.2	odd	4
700.2.t.d.199.16		32	20.7	even	4
700.2.t.d.299.11		32	140.103	odd	12
700.2.t.d.299.16		32	35.33	even	12
980.2.g.a.391.5		32	140.59	even	6
980.2.g.a.391.6		32	140.39	odd	6
980.2.g.a.391.7		32	35.4	even	6
980.2.g.a.391.8		32	35.24	odd	6
980.2.o.f.31.9		32	140.139	even	2
980.2.o.f.31.13		32	35.34	odd	2
980.2.o.f.411.9		32	35.9	even	6
980.2.o.f.411.13		32	140.79	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05472 - 0.942109i) q^{2} +(-0.450639 + 0.780530i) q^{3} +(0.224860 + 1.98732i) q^{4} +(1.21064 - 0.398687i) q^{6} +(-2.29962 + 1.30833i) q^{7} +(1.63511 - 2.30790i) q^{8} +(1.09385 + 1.89460i) q^{9} +(-3.24107 - 1.87123i) q^{11} +(-1.65249 - 0.720054i) q^{12} +2.41990i q^{13} +(3.65805 + 0.786573i) q^{14} +(-3.89888 + 0.893735i) q^{16} +(0.505515 + 0.291859i) q^{17} +(0.631220 - 3.02880i) q^{18} +(-3.07977 - 5.33433i) q^{19} +(0.0151060 - 2.38451i) q^{21} +(1.65551 + 5.02706i) q^{22} +(3.73439 - 2.15605i) q^{23} +(1.06454 + 2.31628i) q^{24} +(2.27981 - 2.55232i) q^{26} -4.67556 q^{27} +(-3.11717 - 4.27589i) q^{28} -0.435463 q^{29} +(-1.26933 + 2.19854i) q^{31} +(4.95421 + 2.73053i) q^{32} +(2.92110 - 1.68650i) q^{33} +(-0.258212 - 0.784080i) q^{34} +(-3.51922 + 2.59985i) q^{36} +(-5.65039 - 9.78676i) q^{37} +(-1.77723 + 8.52769i) q^{38} +(-1.88881 - 1.09050i) q^{39} -7.35068i q^{41} +(-2.26240 + 2.50075i) q^{42} +5.80096i q^{43} +(2.98995 - 6.86180i) q^{44} +(-5.96996 - 1.24418i) q^{46} +(-5.78826 - 10.0256i) q^{47} +(1.05940 - 3.44594i) q^{48} +(3.57652 - 6.01735i) q^{49} +(-0.455610 + 0.263046i) q^{51} +(-4.80912 + 0.544138i) q^{52} +(-1.55746 + 2.69759i) q^{53} +(4.93139 + 4.40489i) q^{54} +(-0.740624 + 7.44657i) q^{56} +5.55147 q^{57} +(0.459290 + 0.410254i) q^{58} +(-1.73534 + 3.00569i) q^{59} +(-8.99597 + 5.19383i) q^{61} +(3.41004 - 1.12299i) q^{62} +(-4.99421 - 2.92575i) q^{63} +(-2.65284 - 7.54735i) q^{64} +(-4.66981 - 0.973217i) q^{66} +(-8.52602 - 4.92250i) q^{67} +(-0.466348 + 1.07025i) q^{68} +3.88640i q^{69} +9.96771i q^{71} +(6.16112 + 0.573383i) q^{72} +(-8.48612 - 4.89946i) q^{73} +(-3.26063 + 15.6456i) q^{74} +(9.90849 - 7.31997i) q^{76} +(9.90142 + 0.0627260i) q^{77} +(0.964785 + 2.92964i) q^{78} +(-0.397549 + 0.229525i) q^{79} +(-1.17456 + 2.03439i) q^{81} +(-6.92515 + 7.75290i) q^{82} +2.59747 q^{83} +(4.74218 - 0.506159i) q^{84} +(5.46514 - 6.11837i) q^{86} +(0.196236 - 0.339892i) q^{87} +(-9.61812 + 4.42040i) q^{88} +(-8.55647 + 4.94008i) q^{89} +(-3.16604 - 5.56486i) q^{91} +(5.12447 + 6.93662i) q^{92} +(-1.14402 - 1.98149i) q^{93} +(-3.34020 + 16.0273i) q^{94} +(-4.36382 + 2.63643i) q^{96} +4.54044i q^{97} +(-9.44122 + 2.97713i) q^{98} -8.18738i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 4 q^{8} - 16 q^{9} + 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} + 8 q^{22} + 36 q^{24} + 30 q^{26} - 2 q^{28} - 40 q^{29} - 2 q^{32} + 60 q^{36} - 8 q^{37} + 60 q^{38} + 62 q^{42}+ \cdots - 78 q^{98}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 - 16 * q^9 + 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 + 8 * q^22 + 36 * q^24 + 30 * q^26 - 2 * q^28 - 40 * q^29 - 2 * q^32 + 60 * q^36 - 8 * q^37 + 60 * q^38 + 62 * q^42 - 18 * q^44 + 2 * q^46 - 16 * q^49 + 36 * q^52 + 8 * q^53 + 12 * q^54 - 4 * q^56 - 48 * q^57 - 2 * q^58 + 24 * q^61 + 4 * q^64 + 24 * q^66 - 60 * q^68 - 4 * q^72 + 72 * q^73 + 38 * q^74 + 40 * q^77 - 120 * q^78 - 36 * q^81 - 42 * q^82 - 20 * q^84 + 28 * q^86 - 4 * q^88 - 60 * q^89 + 4 * q^92 + 8 * q^93 + 18 * q^94 - 60 * q^96 - 78 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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